MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Suspended Romanian Contests
International Mathematical Arhimede Contest (IMAC)
2014 IMAC Arhimede
3
3
Part of
2014 IMAC Arhimede
Problems
(1)
diophantine: 2^x + 21^x = y^3 , 2^x + 21^y = z^2y
Source: IMAC Arhimede 2014 p3
5/6/2019
a) Prove that the equation
2
x
+
2
1
x
=
y
3
2^x + 21^x = y^3
2
x
+
2
1
x
=
y
3
has no solution in the set of natural numbers. b) Solve the equation
2
x
+
2
1
y
=
z
2
y
2^x + 21^y = z^2y
2
x
+
2
1
y
=
z
2
y
in the set of non-negative integer numbers.
number theory
Diophantine equation
Diophantine Equations