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# Modular math.

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What is the smallest positive integer that will satisfy the following:

N mod  1,117 =43,  N mod 3,037 =949,  N mod 2,017 =1,064. Any help would be appreciated. Thank you.

Guest Sep 17, 2017
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### 1+0 Answers

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N mod  1,117 =43,  N mod 3,037 =949,  N mod 2,017 =1,064.

We have the following equalities:

1,117A + 43 = 3,037B + 949 =2,017C + 1,064 =N

By simple iteration we get:

A = 28, B = 10, C = 15. Therefore:

N =1,117 x 28 + 43 = 31, 319

N =3,037 x 10 + 949 = 31,319

N =2,017 x 15 + 1,064 = 31, 319 - which is the smallest positive integer that satisfies all 3 equations.

However, the LCM of {1,117, 3,037, 2,017} =6,842,327,593. It follows that:

N = 6,842,327,593D + 31,319, where D =0, 1, 2, 3, 4.......etc.

Guest Sep 18, 2017

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