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2013 Saudi Arabia Pre-TST
1.2
1.2
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
47 divides 3^x - 2^y iff 23 divides 4x + y.
Source: 2013 Saudi Arabia Pre-TST 1.2
9/13/2020
Let
x
,
y
x, y
x
,
y
be two non-negative integers. Prove that
47
47
47
divides
3
x
ā
2
y
3^x - 2^y
3
x
ā
2
y
if and only if
23
23
23
divides
4
x
+
y
4x + y
4
x
+
y
.
number theory
divides
divisible