Generating Full Period/Full Cycle Random Numbers or Permutations Similar to LCG but without odd/even?

Trivial solution. Make a LCG with R a prime somewhat larger than the range you want, and both a and c somewhere random in that range. If it gives you a number that is larger than you want, iterate again until you are back in range.

If odd/even alternation is your only problem, leave the state change computation unchanged. Before using each output you can either shift the lower bits out or swap the the bits around.

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