Determine for which values of 5 Solutionx is congruent to 3

Solution

x is congruent to 3 mod 7

This means x = 7n+3 for some integer n

n =0 gives x = 3,

n =-1 gives x = -4

Other n give solution outside the interval (-5,5)

Hence solutions are

x =3 and x =-4

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x is congruent to -3 mod 2

x = -3m+2 where m is an integer

m =0 gives x =2, and m = 1 gives x = -1, m = 2, x=-4

m = -1, x =5

Hence there are 4 solutions as

x =2, -1, 5,-4