Fourth Power is Sum of 2 Triangular Numbers/Examples/T41 + T55

Example of Use of Fourth Power is Sum of 2 Triangular Numbers

$7^4 = T_{41} + T_{55}$

Proof

We have:

$41 = 7^2 - 7 - 1$

and:

$55 = 7^2 + 7 - 1$

Hence from Fourth Power is Sum of 2 Triangular Numbers:

$7^4 = T_{41} + T_{55}$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $15$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $15$