If x = 29y+7 and x-y is divisible by 5, then what is the possible value of y where x and y both are integers?

Question

x and y are distinct 2 digit numbers such that y is obtained by reversing the digits of x.
Suppose they also satisfy x^2 - y^2 = m^2 for some positive integer m, then find the value of x+y+m?

Answer 1

One.
x=36 (36=29+7 and
36-1=35 which
divided by 5=7)

Answer 2

we have,
x-y is divisible by 5
say, x-y=5*k
where k be any integer.
x=5k+y................................................(i)
also we have
x = 29y+7
5k+y=29y+7 .............................from (i)
or, 28y=5k-7
or, y=(5k-7)/28............................(ii)

from (ii), it is clear that y will be integer only when (5k-7) is completely divisible by 28.
one of the possible cases is when k=7, then y=(35-7)/28=28/28=1
so, there are infinite number of possible integer values of y.

hence , y=1 is one of the possible values of y.