MathDB
Problems
Contests
International Contests
IMO Longlists
1979 IMO Longlists
24
24
Part of
1979 IMO Longlists
Problems
(1)
All integers n ≥ (a − 1)(b − 1) can be written as n=ua+vb
Source: IMO LongList 1979 - P24
6/1/2011
Let
a
a
a
and
b
b
b
be coprime integers, greater than or equal to
1
1
1
. Prove that all integers
n
n
n
greater than or equal to
(
a
−
1
)
(
b
−
1
)
(a - 1)(b - 1)
(
a
−
1
)
(
b
−
1
)
can be written in the form:
n
=
u
a
+
v
b
,
with
(
u
,
v
)
∈
N
×
N
.
n = ua + vb, \qquad \text{with} (u, v) \in \mathbb N \times \mathbb N.
n
=
u
a
+
v
b
,
with
(
u
,
v
)
∈
N
×
N
.
search
number theory
relatively prime
number theory proposed