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39
Prove that there exist p_i, q_i, r_i - ILL 1990 IRE4
Prove that there exist p_i, q_i, r_i - ILL 1990 IRE4
Source:
September 18, 2010
number theory proposed
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be integers. Prove that there exist integers
p
1
,
q
1
,
r
1
,
p
2
,
q
2
p_1, q_1, r_1, p_2, q_2
p
1
,
q
1
,
r
1
,
p
2
,
q
2
and
r
2
r_2
r
2
, satisfying
a
=
q
1
r
2
−
q
2
r
1
,
b
=
r
1
p
2
−
r
2
p
1
a = q_1r_2 - q_2r_1, b = r_1p_2 - r_2p_1
a
=
q
1
r
2
−
q
2
r
1
,
b
=
r
1
p
2
−
r
2
p
1
and
c
=
p
1
q
2
−
p
2
q
1
.
c = p_1q_2 - p_2q_1.
c
=
p
1
q
2
−
p
2
q
1
.
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