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Israel Team Selection Test
2024 Israel TST
P1
Power diophantine
Power diophantine
Source: 2024 Israel TST Test 2 P1
November 7, 2023
number theory
Diophantine equation
Exponential equation
Problem Statement
Solve in positive integers:
x
y
2
+
1
+
y
x
2
+
1
=
2
z
x^{y^2+1}+y^{x^2+1}=2^z
x
y
2
+
1
+
y
x
2
+
1
=
2
z
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