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Tournament Of Towns
1991 Tournament Of Towns
(291) 1
(291) 1
Part of
1991 Tournament Of Towns
Problems
(1)
TOT 291 1991 Spring O S1 sum x^{2^n} = sum y^{2^n}
Source:
6/9/2024
Find all natural numbers
n
n
n
, and all integers
x
,
y
x,y
x
,
y
(
x
≠
y
x\ne y
x
=
y
) for which the following equation is satisfied:
x
+
x
2
+
x
4
+
.
.
.
+
x
2
n
=
y
+
y
2
+
y
4
+
.
.
.
+
y
2
n
.
x + x^2 + x^4 + ...+ x^{2^n} = y + y^2 + y^4 + ... + y^{2^n} .
x
+
x
2
+
x
4
+
...
+
x
2
n
=
y
+
y
2
+
y
4
+
...
+
y
2
n
.
number theory
diophantine
Diophantine equation