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1971 IMO Longlists
14
14
Part of
1971 IMO Longlists
Problems
(1)
The square of the sum - [IMO LongList 1971]
Source:
1/1/2011
Note that
8
3
ā
7
3
=
169
=
1
3
2
8^3 - 7^3 = 169 = 13^2
8
3
ā
7
3
=
169
=
1
3
2
and
13
=
2
2
+
3
2
.
13 = 2^2 + 3^2.
13
=
2
2
+
3
2
.
Prove that if the difference between two consecutive cubes is a square, then it is the square of the sum of two consecutive squares.
geometry
3D geometry
Diophantine equation
number theory unsolved
number theory