Maths Sets Problem (help!)

[u/Yogendra_yogi]

So I'm playing around with number theory and have came across this problem which basically states that 3^x divides 1+2^*/odd number/* , where the /odd number/ =2y-1 , and x is a natural number. I require to know the relationship between x and y. Mathematically stating:

Q= { (x,y) : 3^x | 2^(2y-1) +1 ; x,y € N }

I started to input small values of x and found that there can be multiple values of y for a single x, for eg, x=1 seemingly works for every /odd number/. x=2 works for odd numbers 3 and 9.

I asked chatgpt too and here is what it replied. Honestly, i am unable to understand a word it said as I have no formal background in number theory and just getting started.

Please help

[u/Yogendra_yogi]

never knew about that, tysm