11*2^n-1+5^n-2+2^n+5^n кратно 13

Question

11*2^n-1+5^n-2+2^n+5^n кратно 13

Answer 1

11*2ⁿ/2+5ⁿ/25+2ⁿ+5ⁿ= 2ⁿ(11/2+1)+5ⁿ(1/25+1)= 2ⁿ*13/2+5ⁿ*26/25= 13(1/2*2ⁿ+2/25*5ⁿ)