Problem Solving (PS) | Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b

hi..

Here we have to remember that \(a^n+b^n\) is always div by a+b when n is ODD

so 58 should tell you that 58=2*29 and the numbers in equation also add up to 29 - 13+16 and 14+15
\(13^7 + 14^7 + 15^7 + 16^7= (13^7+16^7)+(14^7+15^7)\)

two things
1) the entire sum is\(Odd^7+Even^7+Odd^7+Even^7\) .. here total will be EVEN
2) now\(13^7+16^7\) will be div by 13+16=29 and
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