Solve in natural numbers: 3^y+5=2^x.
I can rewrite this equation in: 3(3^b-1)=8(2^a-1), where a=x-3, b=y-1. Then considering LHS with mod 8; and RHS with mod 3, I get that x, y uneven. I know how to solve this problem using idea of monotony by dividing both sides with 3^y. But here is more principal question how to solve this problem using modular arithmetic. So then I was planning to use orders, I mean ord function, but I don’t get new divisors. In this problem x, y are not even, that make it’s much harder to solve. Maybe this links can help:
http://mathhelpplanet.com/viewtopic.php?f=48&t=16911 — similar to my problem.
I can rewrite this equation in: 3(3^b-1)=8(2^a-1), where a=x-3, b=y-1. Then considering LHS with mod 8; and RHS with mod 3, I get that x, y uneven. I know how to solve this problem using idea of monotony by dividing both sides with 3^y. But here is more principal question how to solve this problem using modular arithmetic. So then I was planning to use orders, I mean ord function, but I don’t get new divisors. In this problem x, y are not even, that make it’s much harder to solve. Maybe this links can help: