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National and Regional Contests
PEN Problems
PEN P Problems
25
25
Part of
PEN P Problems
Problems
(1)
P 25
Source:
5/25/2007
Let
a
a
a
and
b
b
b
be positive integers with
gcd
(
a
,
b
)
=
1
\gcd(a, b)=1
g
cd
(
a
,
b
)
=
1
. Show that every integer greater than
a
b
−
a
−
b
ab-a-b
ab
−
a
−
b
can be expressed in the form
a
x
+
b
y
ax+by
a
x
+
b
y
, where
x
,
y
∈
N
0
x, y \in \mathbb{N}_{0}
x
,
y
∈
N
0
.
number theory
relatively prime
Additive Number Theory