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Serbia Team Selection Test
1981 Yugoslav Team Selection Test
Problem 3
Problem 3
Part of
1981 Yugoslav Team Selection Test
Problems
(1)
existence, x+2y+3z+7t=a and y+2z+5t=b
Source: Yugoslav TST 1981 P3
5/29/2021
Let
a
,
b
a,b
a
,
b
be nonnegative integers. Prove that
5
a
>
7
b
5a>7b
5
a
>
7
b
if and only if there exist nonnegative integers
x
,
y
,
z
,
t
x,y,z,t
x
,
y
,
z
,
t
such that \begin{align*} x+2y+3z+7t&=a,\\ y+2z+5t&=b. \end{align*}
Diophantine equation
number theory