Talk:121 (number)

Squares of the form x4 + x3 + x2 + x + 1
Until a couple of minutes before my edits, this page made it seem like it was a conjecture that there are no squares after 121 that are of the form x4 + x3 + x2 + x + 1. This is actually easy to prove!

Case 1: Let x = 2k

Then, x4 + x3 + x2 + x + 1 = 16k4 + 8k3 + 4k2 + 2k + 1. For k > 0, this is between (4k+k)2 and (4k+k+1)2.

Case 2: Let x = 2k+1

Then, x4 + x3 + x2 + x + 1 = 16k4 + 40k3 + 40k2 + 20k + 5. For k > 0, this is between (4k2+k)2 and (4k2+k+1)2. For k > 1, this is between (4k2+5k+1)2 and (4k2+5k+2)2.

As a result, it suffices to check k = 0 and k = 1 and there are no solutions other than x = 0 and x = 3. 173.76.131.225 (talk) 21:32, 18 March 2021 (UTC)
 * I spot a mistake, but more importantly, this is original research. I'll revert your edits for now, but feel free to reinstate them if you can include a reliable source for this information. Gap9551 (talk) 07:43, 19 March 2021 (UTC)

Mera account add kyu nahi ho raha hai
please add my account 45.112.29.69 (talk) 00:27, 25 September 2023 (UTC)


 * For information on creating a Wikipedia account, please see Account. Certes (talk) 12:37, 25 September 2023 (UTC)