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Sweden Contests
Swedish Mathematical Competition
1981 Swedish Mathematical Competition
6
6
Part of
1981 Swedish Mathematical Competition
Problems
(1)
triangles with sides a prime, b power of 2, c square of an odd integer
Source: 1981 Swedish Mathematical Competition p6
3/28/2021
Show that there are infinitely many triangles with side lengths
a
a
a
,
b
b
b
,
c
c
c
, where
a
a
a
is a prime,
b
b
b
is a power of
2
2
2
and
c
c
c
is the square of an odd integer.
number theory
Perfect Square
power of 2
triangle inequality