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
A blog is that is all about mathematics and calculators, two of my passions in life.
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
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