## Sunday, June 16, 2013

### Integers: x^2 + y^2 = n^3, x^3 + y^3 = n^2, x^2 - y^2 = n^3, x^3 - y^3 = n^2

Let x, y, n be integers. I explore x and y for 1 through 15. I use an HP 32Sii to help me with the calculations.

x^2 + y^2 = n^3

2^2 + 2^2 = 2^3
2^2 + 11^2 = 5^3
5^2 + 10^2 = 5^3

Program:

LBL A
x^2
x<>y
x^2
+
3
1/x
y^x
RTN

x^3 + y^3 = n^2

1^3 + 2^3 = 3^2
2^3 + 2^3 = 4^2
8^3 + 4^3 = 24^2
8^3 + 8^3 = 32^2

Program:

LBL B
3
y^x
x<>y
3
y^x
+

RTN

x^2 - y^2 = n^3, x > y

15^2 - 10^2 = 5^3
15^2 - 3^2 = 6^3
14^2 - 13^2 = 3^3
10^2 - 6^2 = 4^3
6^2 - 3^2 = 3^3
3^2 - 1^2 = 2^3

Program:

LBL C
x^2
x<>y
x^2
x<>y
-
3
x√y
RTN

x^3 - y^3 = n^2, x > y

14^3 - 7^3 = 49^2
10^3 - 6^3 = 28^2
8^3 - 7^3 = 13^2

Program:

LBL D
3
y^x
x<>y
3
y^x
x<>y
-

RTN

If you want to find more integer triplets, happy exploring!

To all the dads out there - Happy Father's Day! To my dad, I am so proud of you!

Until next time,

Eddie

Happy One Week from the Summer Solstice!

This blog is property of Edward Shore. 2013