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Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2019 Nigeria Senior MO Round 2
2
Easy divisibility
Easy divisibility
Source: Nigerian senior mathematics Olympiad round 2 problem 2
September 8, 2019
number theory
Problem Statement
Suppose that
p
∣
(
2
t
2
−
1
)
p|(2t^2-1)
p
∣
(
2
t
2
−
1
)
and
p
2
∣
(
2
s
t
+
1
)
p^2|(2st+1)
p
2
∣
(
2
s
t
+
1
)
. Prove that
p
2
∣
(
s
2
+
t
2
−
1
)
p^2|(s^2+t^2-1)
p
2
∣
(
s
2
+
t
2
−
1
)
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