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- ...proximating <math>N(N+1) \approx N^2</math>, we were looking for a perfect square that is close to, but less than, <math>4032</math>. Since <math>63^2 = 3969 Knowing that each row number can stand for the number of coins there are in the row, we can just add until we get <math>2016</mat2 KB (395 words) - 22:29, 3 December 2024
- ...are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four sig For two [[number]]s <math>a</math> and <math>b</math>:12 KB (1,806 words) - 05:07, 19 June 2024
- ...inequality''' is an [[inequality]] that states that the square of any real number is nonnegative. Its name comes from its simplicity and straightforwardness. For all [[real number]]s <math>x</math>, <math>x^2 \ge 0</math>.3 KB (583 words) - 20:20, 2 August 2024
- ...s the highest power of the variable which appears in the polynomial. This number is known as the ''degree'' of the polynomial and is written <math>\deg(P)</ ...Fundamental Theorem of Algebra]] states that any polynomial with [[complex number|complex]] coefficients can be written as6 KB (1,100 words) - 14:57, 30 August 2024
- ...olve more than algebra problems, sometimes going into other topics such as number theory. *Two different [[prime number]]s between <math>4</math> and <math>18</math> are chosen. When their sum is4 KB (682 words) - 12:13, 8 December 2024
- ===Proof that the square root of 2 is irrational=== Assume <math>\sqrt{2}</math> is [[rational number|rational]], i.e. it can be expressed as a rational fraction of the form <ma2 KB (374 words) - 13:01, 21 August 2022
- ...must be incorrect; at least one box must contain two or more balls. <math>\square</math> ...ber of red, blue, yellow, and black socks in a drawer, what is the minimum number of socks that the Martian must pull out of the drawer to guarantee they hav11 KB (1,986 words) - 18:13, 19 June 2024
- ...th>x</math> such that <math>P = x^4 + 6x^3 + 11x^2 + 3x + 31</math> is the square of an integer. Then <math>n</math> is: ...say <math>P=(x^2+3x+1)^2-3(x-10)=a^2</math>, where <math>a^2</math> is the square of an integer mentioned on the problem. Right from here, we can set <math>x3 KB (571 words) - 23:42, 21 October 2021
- '''Number theory''' is the field of [[mathematics]] associated with studying the prop Number theory is a broad topic, and may cover many diverse subtopics, such as:3 KB (404 words) - 19:56, 28 December 2024
- '''Fermat's Little Theorem''' is highly useful in [[number theory]] for simplifying the computation of exponents in [[modular arithmet If <math>{a}</math> is an [[integer]], <math>{p}</math> is a [[prime number]] and <math>{a}</math> is not [[divisibility|divisible]] by <math>{p}</math16 KB (2,660 words) - 22:42, 28 August 2024
- ...]]. If <math>n</math> is a positive integer, <math>\phi{(n)}</math> is the number of integers in the range <math>\{1,2,3\cdots{,n}\}</math> which are relativ ...}</math> is allowed since it is relatively prime to <math>m</math>. <math>\square</math>4 KB (569 words) - 21:34, 30 December 2024
- ...ed equal to <math>\frac{n(n+1)}{2}</math> (the <math>n</math>th triangular number is defined as <math>1+2+\cdots +n</math>; imagine an [[equilateral polygon ...n can be useful in almost any branch of mathematics. Often, problems in [[number theory]] and [[combinatorics]] are especially susceptible to induction solu5 KB (768 words) - 23:59, 28 September 2024
- ...ve at our answer: <math>9 \cdot 10 \cdot 10 \cdot 10 = 9000</math>. <math>\square</math> ...ht lead one to think. All we did was think about constructing a four-digit number by choosing its digits, compute the possible numbers each digit can be, and13 KB (2,018 words) - 14:31, 10 January 2025
- ...n four letters long and contain only the letters A, B, C, D, and E. <math>\square</math> ...<math>68+53=121</math> positive integer solutions to the equation. <math>\square</math>5 KB (709 words) - 16:40, 24 September 2024
- A '''prime number''' (or simply '''prime''') is a [[positive integer]] <math>p>1</math> whose ...osite number|composite]] because it is its only factor among the [[natural number|natural numbers]].6 KB (1,053 words) - 20:29, 7 January 2025
- ...ative. The range is the set of all non-negative real numbers, because the square root can never return a negative value.10 KB (1,761 words) - 02:16, 12 May 2023
- ...where one counts what they don't want, then subtracts that from the total number of possibilities. In problems that involve complex or tedious [[casework]], ...>19</math> of them. Thus, our answer is is <math>99-19 = 80</math>. <math>\square</math>8 KB (1,192 words) - 16:20, 16 June 2023
- ...o choose <math>k-1</math> things from <math>n-1</math> things added to the number of ways to choose <math>k</math> things from <math>n-1</math> things. &=&\binom{n}{k}. \qquad\qquad\square\end{eqnarray*}</cmath>12 KB (1,993 words) - 22:47, 27 October 2024
- ...tosthenes''' is a simple method to quickly uncover a short list of [[prime number]]s. ...aximal number you are interested in. Now, during each step, take the first number that is neither crossed out nor circled, circle it, and cross all larger nu1 KB (212 words) - 20:16, 7 December 2007
- ...n=kd</math> or, in other words, if <math>\frac nd</math> is also a natural number (i.e <math>d</math> divides <math>n</math>). See [[Divisibility]] for more A common notation to indicate a number is a divisor of another is <math>n|k</math>. This means that <math>n</math>1 KB (274 words) - 18:50, 29 August 2023