+0  
 
0
135
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar
0

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

10 Online Users

avatar

New Privacy Policy (May 2018)

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see cookie policy and privacy policy.