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In this problem, m and n are integers. If m= 4 mod 14 and m-n=10 mod 14, then what is the remainder when m+n is divided by 14?

 

Suppose x-3 and y+3 are multiples of 7. What is the smallest positive integer, n, for which x^2+xy+y^2+n is a multiple of 7?

 

Please help, thanks!

 May 11, 2020
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I bet you are taking Introduction to Number Theory AOPS Alcumus section because I got the same question ._.

 May 14, 2020

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