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Pan African
2017 Pan African
Problem 3
Problem 3
Part of
2017 Pan African
Problems
(1)
Problem 3 number of solutions for integer equation
Source: PAMO 2017 Problem 3
7/5/2017
Let
n
n
n
be a positive integer. - Find, in terms of
n
n
n
, the number of pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of positive integers that are solutions of the equation :
x
2
ā
y
2
=
1
0
2
.
3
0
2
n
x^2-y^2=10^2.30^{2n}
x
2
ā
y
2
=
1
0
2
.3
0
2
n
- Prove further that this number is never a square
number theory
PAMO