
Hi
Can someone please help me out with the following question ?
In how many ways can a pair of natural numbers be selected from a set containing the first 91 natural numbers such that their sum is a multiple of 13?
I followed the following approach 
a + b = 13 ,since a and b can not be zero ,they will take the value atleast 1. No of solutions = 11 + 2  1 C 2 1 = 12
a + b = 26 , will have 25  1 solutions since we can not take 13,13
a + b = 39  38 solutions
a + b = 52  50 solutions
a + b = 65  62 solutions
a + b = 78  76 solutions
a + b = 91  90 solutions
Total = 12 + 24 + 38 + 50 + 62 + 76 + 90 = 352
But the answer is 315 , I cant figure out what am I doing wrong , please advise . 