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2013 IMAC Arhimede
1
1
Part of
2013 IMAC Arhimede
Problems
(1)
a^5b^3-a^3b^5 is a mutliple of 10
Source: IMAC Arhimede 2013 p1
5/6/2019
Show that in any set of three distinct integers there are two of them, say
a
a
a
and
b
b
b
such that the number
a
5
b
3
ā
a
3
b
5
a^5b^3-a^3b^5
a
5
b
3
ā
a
3
b
5
is a multiple of
10
10
10
.
number theory
multiple
divisible