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Tournament Of Towns
1991 Tournament Of Towns
(291) 1
TOT 291 1991 Spring O S1 sum x^{2^n} = sum y^{2^n}
TOT 291 1991 Spring O S1 sum x^{2^n} = sum y^{2^n}
Source:
June 9, 2024
number theory
diophantine
Diophantine equation
Problem Statement
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
.
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