math - How will be changed the number by dividing the absolute value for storing the result of changing the divider? -


here formula:

result = (const + var) % mod

result - interger, >= 0

const, var, mod - interger, > 0

question:

how calculate var if:

  • mod incremented
  • mod decremented

result и const won't changed.

not bruteforce.

found solution.

result = (const + var) % mod

let, newmod - incremented or decremented mod.

var = newmod - (const - result) % newmod

examples.

with original formula.

(25 + 15) % 16 = 8
  • const = 25
  • var = 15
  • mod = 16
  • result = 8

incremented:

newmod = mod + 1 = 17  var = 17 - (25 - 8) % 17 = 17 - 0 = 17  (25 + 17) % 17 = 8

decremented:

newmod = mod - 1 = 15  var = 15 - (25 - 8) % 15 = 15 - 2 = 13  (25 + 13) % 15 = 8

upd: proof.

we need substract result both parts.

because that's not division (just remainder of division) can this.

const + var >= result

, result remainder of division

(25 - 8 + var) % 16 = 0 => (17 + var) % 16 = 0

in other words (a special case):

17 + var = 16 => var = 16 - 17 = -1  (25 + (-1)) % 16 = 8

the answer in not 1 - numbers intervals of newmod.

in case: -1, 15, 31, 47 etc.


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