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2015 Israel National Olympiad
Problems
(1)
Israel 2015 Q1 - Timely diophantine equation
Source: Israel National Olympiad 2015 Q1
8/7/2019
[*] Find an example of three positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfying
31
a
+
30
b
+
28
c
=
365
31a+30b+28c=365
31
a
+
30
b
+
28
c
=
365
. [*] Prove that any triplet
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfying the above condition, also satisfies
a
+
b
+
c
=
12
a+b+c=12
a
+
b
+
c
=
12
.
Diophantine equation
number theory
algebra