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National and Regional Contests
Bolivia Contests
Bolivian Ibero TST
2021 Bolivia Ibero TST
3
3
Part of
2021 Bolivia Ibero TST
Problems
(1)
a,b,c cubed give different residues modulo p
Source: Bolivia Ibero TST 2021 Day 2 P1
9/2/2022
Let
p
=
a
b
+
b
c
+
a
c
p=ab+bc+ac
p
=
ab
+
b
c
+
a
c
be a prime number where
a
,
b
,
c
a,b,c
a
,
b
,
c
are different two by two, show that
a
3
,
b
3
,
c
3
a^3,b^3,c^3
a
3
,
b
3
,
c
3
gives different residues modulo
p
p
p
number theory
modular arithmetic
Bolivia
TST
prime numbers