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.
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.
