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Bulgaria Team Selection Test
2020 Bulgaria Team Selection Test
2
2
Part of
2020 Bulgaria Team Selection Test
Problems
(1)
Multiple of power of two.
Source: Bulgarian TST, 2020, p2
8/4/2020
Given two odd natural numbers
a
,
b
a,b
a
,
b
prove that for each
n
∈
N
n\in\mathbb{N}
n
∈
N
there exists
m
∈
N
m\in\mathbb{N}
m
∈
N
such that either
a
m
b
2
−
1
a^mb^2-1
a
m
b
2
−
1
or
b
m
a
2
−
1
b^ma^2-1
b
m
a
2
−
1
is multiple of
2
n
.
2^n.
2
n
.
algebra
number theory
TST
Bulgaria