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b|2a + 1, c|2b + 1, a|2c + 1 - All-Russian MO 2000 Regional (R4) 9.2

Source:

September 26, 2024

number theorydivisibledivides

Problem Statement

Are there different mutually prime natural numbers

a

b

and

c

, greater than

1

, such that

2a + 1

is divisible by

b

2b + 1

is divisible by

c

and

2c + 1

is divisible by

a