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Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems"

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==Problem 2==
 
==Problem 2==
  
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Determine all positive integers <math>a</math> such that <math>a < 100</math> and <math>a^3 + 23</math> is divisible by <math>24</math>.
  
 
[[2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2|Solution]]
 
[[2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2|Solution]]

Revision as of 05:16, 19 January 2019

UNM - PNM STATEWIDE MATHEMATICS CONTEST L. February 3, 2018. Second Round. Three Hours

Problem 1

Let $x \ne y$ be two real numbers. Let $x,a_1,a_2,a_3,y$ and $b_1,x,b_2,b_3,y,b_4$ be two arithmetic sequences.

Calculate $\frac{b_4-b_3}{a_2-a_1}$.


Solution

Problem 2

Determine all positive integers $a$ such that $a < 100$ and $a^3 + 23$ is divisible by $24$.

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

See Also

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