Determine the smallest positive integer such that 60^n+k*71^n is divisible by 1441 for all odd positive integers n

Guest Jul 18, 2019

#1**+4 **

Does this problem let usage of a calculator? Because I used a calculator to discover that *the factors of 1441 are 131 and 11*.

*To check if a number is prime

So knowing that 131 and 11 multiply to 1441, we can see that miraculously if you substitute **1 **for n in your equation 60^{n }+ k * 71^{n} you get 131*k. And since 11 multiplied by 131 is 1441, **k should be \(\boxed{11}\)**.

CalculatorUser Jul 18, 2019

edited by
CalculatorUser
Jul 18, 2019

edited by CalculatorUser Jul 18, 2019

edited by CalculatorUser Jul 18, 2019

edited by CalculatorUser Jul 18, 2019

edited by CalculatorUser Jul 18, 2019