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Baltic Way
1993 Baltic Way
2
2
Part of
1993 Baltic Way
Problems
(1)
an+b is the k-th power of some integer
Source: Baltic Way 1993
6/15/2012
Do there exist positive integers
a
>
b
>
1
a>b>1
a
>
b
>
1
such that for each positive integer
k
k
k
there exists a positive integer
n
n
n
for which
a
n
+
b
an+b
an
+
b
is a
k
k
k
-th power of a positive integer?
modular arithmetic
number theory proposed
number theory