A few years ago I boldly introduced a new term called "skewy", which I defined as the smallest square root of (n+1/2)2 mod n where n is the product of two distinct odd primes.
The skewy has an interesting relation to the Collatz conjecture and to the prime factorization of n.
Here are a few claims to consider:
Claim #1: 4*((n+1)/2)2 = 1 mod n
Claim #2: The row at 4 of the exponentiation table of Zn consists of all squares co-prime with n.
Claim #4: If s is the skewy, then 4*(s3 mod n) mod n = s.
Claim #5: 4*(((n+1)/2)3 mod n) mod n = (n+1)/2.
19.3.19
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