41, 80 and 320?

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- Jul 19th 2010, 10:56 AMwonderboy1953What do these numbers have in common?
41, 80 and 320?

- Jul 19th 2010, 06:42 PMSoroban

Um . . . Their binary representations begin with "101" ?

. . $\displaystyle \begin{array}{ccc} 41 &=& 101001_2 \\

80 &=& 1010000_2 \\

320 &=& 101000000_2 \end{array}$

- Jul 19th 2010, 06:43 PMbigblackbronco
they can all be / by 1

- Jul 20th 2010, 06:12 AMSoroban

Don't know how I missed that . . .

Quote:

Originally Posted by**bigblackbronco**

And I wasted all that time looking for patterns . . . *sigh*

. . $\displaystyle \begin{array}{ccc}

41 &=& 4^2 + 5^2 \\

80 &=& 4^2 + 8^2 \\

320 &=& 8^2 + 16^2 \end{array}$

- Jul 20th 2010, 10:14 AMwonderboy1953
Keep going.

- Jul 20th 2010, 02:24 PMeumyang
If you add the three numbers you get a perfect square:

$\displaystyle 41 + 80 + 320 = 441 = 21^2$

And... if you add any two of the numbers you also get perfect squares:

$\displaystyle \begin{aligned}

41 + 80 &= 121 = 11^2 \\

80 + 320 &= 400 = 20^2 \\

41 + 320 &= 361 = 19^2

\end{aligned}$

If it wasn't for Soroban's last post I wouldn't have thought of this. (Bow) - Jul 20th 2010, 04:20 PMwonderboy1953
- Aug 2nd 2010, 08:23 AMChokfull