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Let x and y be integers satisfying 41x + 53y = 18. Find the residue of x modulo 53.
(Express your answer as an integer from 0 to 52.)

 Dec 10, 2020
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 41x + 53y = 18

 

x = 25,    y = - 19

 

25 mod 53 = 25

 

Note: There are an infinite number of solutions for x and y. They should have specified the pair, such as: the "smallest pair", which is what I used. There is also a solution where x =- 28 and y = 22, in which case:

 

-28 mod 53 = - 28

53 + (-28) ==25.  In either case , the answer appears to be 25.

 Dec 10, 2020

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