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January 31
Why does this algorithm always lead to the trivial square root of Template:Math when Template:Math is a perfect square?
This is based on Talk:Kunerth's algorithm#Taking The Square Root of 67*Y Mod RSA260
First take , a random semiprime… then use the following pseudocode :
2. Compute :
3. Find integers and such as (25²+ x×digitsConstant)÷(y×67) = digitsConstant+bb
4. take , an unknown variable, then expand ((67z + 25)²+ x×digitsConstant)÷(y×67) and then take the last Integer part without a called . will always be a perfect square.
5.
6. Find and such as a== w (25 + w×b)
7. Solve 0=a²×x²+(2a×b−(x×digitsConstant))×z+(b²−67×y)
8. For each of the 2 possible integer solution, compute z mod digitsConstant.
The fact the result will be a modular square root is expected, but then why if the computed at step 2 is a perfect square, z mod\ digitsConstant will always be the same as the Integer square root of and not the other possible modular square ? (that is, the trivial solution). 2A01:E0A:401:A7C0:9CB:33F3:E8EB:8A5D (talk) 09:22, 31 January 2025 (UTC)
Numbers m such that there is n such that eulerphi(eulerphi(n)) = m but there is no number with exactly m primitive roots
56 is in the range of eulerphi(eulerphi(n)), but there is no number with exactly 56 primitive roots, the numbers like 56 seems to be rare, what is the set of such numbers (i.e. the intersection of Template:OEIS and Template:OEIS) <= 10000? 220.132.216.52 (talk) 17:16, 31 January 2025 (UTC)