Loading [MathJax]/extensions/TeX/mathchoice.js

Monday, October 4, 2021

2020/080) Solve in integer x 5^x - 3^x = 16

Working mod 3 we have (-1)^x\equiv 1 \pmod 3

So x is even say 2n

So we have ^{2n} - 3^{2n} = 16

Or (5^n+3^n)(5^n-3^n) =16

On  LHS both are even and unequal and 1st term is larget and 16 need to be factored into 2 even numbers 8 * 2

So 5^n +3^n = 8

5^n - 3^n = 2

Adding we get 2* 5^n = 10 or n = 1 so x = 2

  

  

No comments: