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Problems
Contests
National and Regional Contests
Iran Contests
Pre-Preparation Course Examination
2007 Pre-Preparation Course Examination
7
7
Part of
2007 Pre-Preparation Course Examination
Problems
(1)
Two sets- Iran 3rd round-Number Theory 2007
Source:
7/28/2010
Let
p
p
p
be a prime such that
p
≡
3
(
m
o
d
4
)
p \equiv 3 \pmod 4
p
≡
3
(
mod
4
)
. Prove that we can't partition the numbers
a
,
a
+
1
,
a
+
2
,
⋯
,
a
+
p
−
2
a,a+1,a+2,\cdots,a+p-2
a
,
a
+
1
,
a
+
2
,
⋯
,
a
+
p
−
2
,(
a
∈
Z
a \in \mathbb Z
a
∈
Z
) in two sets such that product of members of the sets be equal.
modular arithmetic
inequalities
number theory unsolved
number theory