Solve the congruence: x^37 is congruent with 12 (mod 5)  

Expert Answers

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You need to use the definition of congruence such that:

`x^37 -= 12`  mod 5 if `5| (x^37 - 12)`

Notice that this is not a linear congruence but you may try x = 0, x= 1, ...., x = 4.

`x = 1 =gt 5`  does not divide 11

`x = 2 =gt 2^37 - 12`  is not divisible by 5

`x = 3 =gt 3^37 - 12`  is not divisible by 5

`x = 4 =gt 4^37 - 12`  is not divisible by 5

Hence, there are not x integer values to satisfy the congruence equation.

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