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National and Regional Contests
Argentina Contests
Argentina National Olympiad
2010 Argentina National Olympiad
3
3
Part of
2010 Argentina National Olympiad
Problems
(1)
min max of a+b+c if a^2+b^2=c^2+99^2 for integers 0<a,b,c <99
Source: 2010 Argentina OMA Finals L3 p3
1/15/2023
The positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
are less than
99
99
99
and satisfy
a
2
+
b
2
=
c
2
+
9
9
2
a^2+b^2=c^2+99^2
a
2
+
b
2
=
c
2
+
9
9
2
. . Find the minimum and maximum value of
a
+
b
+
c
a+b+c
a
+
b
+
c
.
algebra
inequalities
number theory