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South Africa Contests
South Africa National Olympiad
2012 South africa National Olympiad
4
4
Part of
2012 South africa National Olympiad
Problems
(1)
x^k + px = y^k
Source: SAMO Senior Round 3 2012 Problem 4
9/6/2012
Let
p
p
p
and
k
k
k
be positive integers such that
p
p
p
is prime and
k
>
1
k>1
k
>
1
. Prove that there is at most one pair
(
x
,
y
)
(x,y)
(
x
,
y
)
of positive integers such that
x
k
+
p
x
=
y
k
x^k+px=y^k
x
k
+
p
x
=
y
k
.
function
number theory unsolved
number theory