4

Part of 2021 New Zealand MO

Problems(2)

diophantine 2x(x + 5) = p^n + 3(x - 1)

Source: New Zealand MO 2021 Round 1 p4

Find all triples

(x, p, n)

of non-negative integers such that

p

2x(x + 5) = p^n + 3(x - 1)

Diophantine equationdiophantinenumber theory

Source: NZMO 2

AB

be a chord of circle

\Gamma

O

be the centre of a circle which is tangent to

AB

C

and internally tangent to

\Gamma

P

C

A

B

. Let the circumcircle of triangle

POC

\Gamma

at distinct points

P

Q

\angle{AQP}=\angle{CQB}