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Part of PEN H Problems

Problems(1)

Source:

a, b, c

be positive integers such that

a

b

are relatively prime and

c

is relatively prime either to

a

b

. Prove that there exist infinitely many triples

(x, y, z)

of distinct positive integers such that

x^{a}+y^{b}= z^{c}.

modular arithmeticnumber theoryrelatively primeDiophantine Equations