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 Wikipedia:Account. Certes (talk) 12:37, 25 September 2023 (UTC)