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ASU 430 All Soviet Union MO 1986 a^2 + b = c, find three no with equal digits

Source:

August 6, 2019

Digitsnumber theory

Problem Statement

The decimal notation of three natural numbers consists of equal digits:

n

digits

x

for

a

n

digits

y

for

b

and

2n

digits

z

for

c

. For every

n > 1

find all the possible triples of digits

x,y,z

such, that

a^2 + b = c