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• 11:46, 15 January 2020 (diff | hist) . . (+916)‎ . . 2006 iTest Problems/Problem 19 ‎ (→‎Solution)
• 11:43, 15 January 2020 (diff | hist) . . (-2)‎ . . 2006 SMT/General Problems/Problem 16 ‎ (→‎Solution) (current)
• 11:43, 15 January 2020 (diff | hist) . . (+71)‎ . . 2006 SMT/General Problems/Problem 16 ‎ (→‎Solution)
• 11:37, 15 January 2020 (diff | hist) . . (+2)‎ . . m 2006 SMT/Calculus Problems/Problem 2 ‎ (→‎Solution) (current)
• 17:39, 14 January 2020 (diff | hist) . . (+96)‎ . . 2006 SMT/Team Problems/Problem 8 ‎ (→‎Solution) (current)
• 17:38, 14 January 2020 (diff | hist) . . (+275)‎ . . m 2006 SMT/Team Problems/Problem 13 ‎ (→‎Solution) (current)
• 17:37, 14 January 2020 (diff | hist) . . (+282)‎ . . m 2006 SMT/Team Problems/Problem 15 ‎ (→‎Solution) (current)
• 17:37, 14 January 2020 (diff | hist) . . (0)‎ . . m 2006 SMT/General Problems/Problem 8 ‎ (→‎Solution) (current)
• 17:36, 14 January 2020 (diff | hist) . . (+12)‎ . . m 2006 SMT/General Problems/Problem 8 ‎ (→‎Solution)
• 17:36, 14 January 2020 (diff | hist) . . (+104)‎ . . m 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution) (current)
• 17:35, 14 January 2020 (diff | hist) . . (-2)‎ . . m 2006 SMT/General Problems/Problem 8 ‎ (→‎Problem 8)
• 17:35, 14 January 2020 (diff | hist) . . (+311)‎ . . m 2006 SMT/General Problems/Problem 16 ‎ (→‎Solution)
• 17:34, 14 January 2020 (diff | hist) . . (+269)‎ . . m 2006 SMT/General Problems/Problem 13 ‎ (→‎Solution) (current)
• 17:33, 14 January 2020 (diff | hist) . . (+325)‎ . . 2006 SMT/General Problems/Problem 8 ‎ (→‎Solution)
• 17:32, 14 January 2020 (diff | hist) . . (+91)‎ . . m 2006 SMT/Calculus Problems/Problem 6 ‎ (→‎Solution) (current)
• 17:31, 14 January 2020 (diff | hist) . . (+60)‎ . . m 2006 SMT/Calculus Problems/Problem 5 ‎ (→‎Solution) (current)
• 17:31, 14 January 2020 (diff | hist) . . (+158)‎ . . m 2006 SMT/Calculus Problems/Problem 2 ‎ (→‎Solution)
• 17:30, 14 January 2020 (diff | hist) . . (-59)‎ . . m 2006 SMT/Advanced Topics Problems/Problem 10 ‎ (→‎Problem 10) (current)
• 17:30, 14 January 2020 (diff | hist) . . (+157)‎ . . m 2006 SMT/Advanced Topics Problems/Problem 10 ‎ (→‎Solution)
• 17:27, 14 January 2020 (diff | hist) . . (+532)‎ . . 2006 iTest Problems/Problem 37 ‎ (→‎Solution) (current)
• 17:27, 14 January 2020 (diff | hist) . . (+532)‎ . . 2006 iTest Problems/Problem 20 ‎ (→‎Solution)
• 17:26, 14 January 2020 (diff | hist) . . (+532)‎ . . 2006 iTest Problems/Problem 19 ‎ (→‎Solution)
• 17:19, 14 January 2020 (diff | hist) . . (+565)‎ . . N 2006 SMT/General Problems/Problem 16 ‎ (Created page with "==Solution== The condition we are looking for is <math>35(n-1)\equiv 0 \mod 360</math>, because if any other <math>A_n = A_1</math> than <math>35(n-1)</math> must be a multip...")
• 17:06, 14 January 2020 (diff | hist) . . (+14)‎ . . m 2006 SMT/General Problems/Problem 12 ‎ (current)
• 17:01, 14 January 2020 (diff | hist) . . (+316)‎ . . N 2006 SMT/General Problems/Problem 12 ‎ (Created page with "Noticing that the sum of the digits of 8091 is 18, we can divide 8091 by 9, yielding 899. Testing all prime numbers up to <math>\sqrt{899} \approx 30</math>, we see that 899 i...")
• 16:53, 14 January 2020 (diff | hist) . . (+977)‎ . . N 2006 SMT/Advanced Topics Problems/Problem 10 ‎ (Created page with "==Solution== First of all, remember that <cmath>\arctan(a)+\arctan(b) = \arctan(\frac{a+b}{1-ab}) +k\pi </cmath> Therefore we want <math>a</math> and <math>b</math> such tha...")
• 16:15, 14 January 2020 (diff | hist) . . (+610)‎ . . N 2006 SMT/Calculus Problems/Problem 5 ‎ (Created page with "==Solution== Using integration by parts, we find that the desired integral is equal to: <cmath>\begin{align*} \int(x\tan^{-1}x)dx &= \frac{x^2}{2}\tan^{-1}x-\int\frac{x^2}{2...")
• 15:56, 14 January 2020 (diff | hist) . . (+699)‎ . . N 2006 SMT/Calculus Problems/Problem 2 ‎ (Created page with "==Solution== Substituting <math>y=e^{\lambda t}</math> into the differential equation, we can solve for the values of <math>\lambda</math>: <cmath>\begin{align*} 0&=4y''+3y'...")
• 14:31, 14 January 2020 (diff | hist) . . (+1,032)‎ . . N 2006 SMT/Calculus Problems/Problem 6 ‎ (Created page with "==Solution== Let <math>u=\frac{\pi}{2}-x</math> and <math>du=-dx</math>, the integral than turns into: <cmath> I = \int_{0}^{\pi/2}\frac{\sin^3x}{\sin^3x+\cos^3x}dx \Rightar...")
• 14:09, 14 January 2020 (diff | hist) . . (+2,190)‎ . . N 2006 iTest Problems/Problem 20 ‎ (Created page with "==Solution== <asy> unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2));...")
• 13:56, 14 January 2020 (diff | hist) . . (+2,181)‎ . . N 2006 iTest Problems/Problem 19 ‎ (Created page with "==Solution== <asy> unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2));...")
• 13:12, 14 January 2020 (diff | hist) . . (+625)‎ . . N 2006 SMT/Team Problems/Problem 6 ‎ (Created page with "==Solution== Rewriting <math> 16^n+4^n+1 </math> as <math>2^{4n}+2^{2n}+1</math> we can set the two given expressions equal to each other. <cmath>\begin{align*} \frac{(2^{p(...") (current)
• 12:59, 14 January 2020 (diff | hist) . . (+1,084)‎ . . N 2006 SMT/Team Problems/Problem 8 ‎ (Created page with "==Solution== To begin, let's rewrite the sum as <cmath>\lim_{n\to\infty} \sum_{k=n^2}^{(n+1)^2} \frac{1}{\sqrt{k}} = \lim_{n\to\infty} \sum_{k=0}^{2n+1} \frac{1}{\sqrt{n^2+...")
• 12:43, 14 January 2020 (diff | hist) . . (+1,220)‎ . . N 2006 SMT/Team Problems/Problem 13 ‎ (Created page with "==Solution== A line that passes through the origin has an equation of <math>y=mx</math>. If the line <math>y=mx</math> is tangent to the hyperbola than the equation <math>(mx...")
• 12:26, 14 January 2020 (diff | hist) . . (+2,599)‎ . . N 2006 SMT/Team Problems/Problem 15 ‎ (Created page with "==Solution== Denote <math>\prod_{i=0}^{\infty} \frac{c_i^{2}}{c_i^{2}-1}</math> as <math>\prod_{composite} \frac{c^2}{c^2-1}</math>. To begin, let <math>S</math> = <math>\pro...")
• 17:36, 13 January 2020 (diff | hist) . . (+544)‎ . . N 2006 SMT/General Problems/Problem 14 ‎ (Created page with "==Solution== Noticing that the first equation, <math>x^2+y^2\le\pi^2</math> is the equation of a disk of radius <math>\pi</math>, and that the graph of <math>y = sin(x)</math...") (current)
• 17:20, 13 January 2020 (diff | hist) . . (+245)‎ . . N 2006 SMT/General Problems/Problem 13 ‎ (Created page with "==Solution== This solution does require quite a bit of guessing and testing, but if we notice that we want the numbers to be relatively close so that no term "dominates" the...")
• 17:10, 13 January 2020 (diff | hist) . . (+9)‎ . . m 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 17:10, 13 January 2020 (diff | hist) . . (+9)‎ . . m 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 17:09, 13 January 2020 (diff | hist) . . (+58)‎ . . 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 17:06, 13 January 2020 (diff | hist) . . (+2)‎ . . m 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 17:06, 13 January 2020 (diff | hist) . . (+15)‎ . . 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 17:06, 13 January 2020 (diff | hist) . . (+316)‎ . . 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution)
• 16:59, 13 January 2020 (diff | hist) . . (-567)‎ . . 2006 SMT/General Problems/Problem 10 ‎ (→‎Solution) (Tag: Replaced)
• 16:58, 13 January 2020 (diff | hist) . . (+579)‎ . . N 2006 SMT/General Problems/Problem 10 ‎ (Created page with "==Solution== First of all, lets note that the sum of all positive integers from <math>1</math> to <math>n</math> inclusive is <math>\frac{n(n+1)}{2}</math>. The sum of all nu...")
• 16:42, 13 January 2020 (diff | hist) . . (+1,227)‎ . . N 2006 SMT/General Problems/Problem 8 ‎ (Created page with "==Solution== Assuming all the numbers are positive, lets denote the five numbers as <math>a_0,a_1,a_2,a_3,a_4</math>. Assume WLOG that <math>a_0 \ge a_1 \ge a_2 \ge a_3 \ge a...")
• 15:55, 13 January 2020 (diff | hist) . . (+754)‎ . . N 2013 PMWC Problems/Problem I15 ‎ (Created page with "==Solution== First of all, note that <math>M=\sum_{n=1}^\infty \frac{1}{k^2}</math>, and that <math>K=\sum_{n=1}^\infty \frac{1}{(2k-1)^2}</math> Splitting <math>M</math> in...") (current)
• 15:02, 13 January 2020 (diff | hist) . . (+2,801)‎ . . N 2006 iTest Problems/Problem 37 ‎ (Created page with "==Solution== To begin, let's number the equations as follows <cmath>\begin{align} x^2 + xy + y^2 &= 1 \\ y^2 + yz +z^2 &= 2 \\ z^2 + zx +x^2 &= 3 \end{align}</cmath> In or...")
• 15:02, 13 January 2020 (diff | hist) . . (-2,802)‎ . . 2006 iTest Problems ‎ (→‎Solution)
• 15:01, 13 January 2020 (diff | hist) . . (+2,803)‎ . . 2006 iTest Problems ‎ (→‎Problem 37)

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