MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN S Problems
23
S 23
S 23
Source:
May 25, 2007
Miscellaneous Problems
Problem Statement
Observe that
1
1
+
1
3
=
4
3
,
4
2
+
3
2
=
5
2
,
\frac{1}{1}+\frac{1}{3}=\frac{4}{3}, \;\; 4^{2}+3^{2}=5^{2},
1
1
+
3
1
=
3
4
,
4
2
+
3
2
=
5
2
,
1
3
+
1
5
=
8
15
,
8
2
+
15
2
=
17
2
,
\frac{1}{3}+\frac{1}{5}=\frac{8}{15}, \;\; 8^{2}+{15}^{2}={17}^{2},
3
1
+
5
1
=
15
8
,
8
2
+
15
2
=
17
2
,
1
5
+
1
7
=
12
35
,
12
2
+
35
2
=
37
2
.
\frac{1}{5}+\frac{1}{7}=\frac{12}{35}, \;\;{12}^{2}+{35}^{2}={37}^{2}.
5
1
+
7
1
=
35
12
,
12
2
+
35
2
=
37
2
.
State and prove a generalization suggested by these examples.
Back to Problems
View on AoPS