Finding next input for a function that would return the same result

[theramsnake]

Hello, I have a problem that I am trying to solve for weeks:

Given a value y such that y%64=0.
And a function f(x)=x%14699+round_down(x/400)%53

How to find smallest possible d such that:
f(y) = f(y+d). And (y+d)%64=0

Any help would be appreciated. Thank you.

 

[stapel]

Hello, I have a problem that I am trying to solve for weeks:

Given a value y such that y%64=0.
And a function f(x)=x%14699+round_down(x/400)%53

How to find smallest possible d such that:
f(y) = f(y+d). And (y+d)%64=0

Any help would be appreciated. Thank you.

What are you using the percentage symbol ("%") to stand for?

When you reply, please specify the course that generated this question (algebra? number theory?), and your level of study (high school? grad school?), and include your thoughts and efforts so far, even if you think they're wrong.

Thank you!

 

[theramsnake]

I am software engineer and solving a problem which I cannot reveal due to nda. My education is just a school education of Soviet Union, no extra math education.
'%' stands for a mod division operation.
My current approach is to increment 'd' by one until f(y+d) gives me same as f(y) and (y%d)=0. Which is very bad.
I was trying to find a larger step for d, by multiplying constants in the formula in different ways with no success. I also tried to generate the values of each f(y+d) to see that maybe there is pattern i can follow with no success. For each next value that satisfies my condition there is a different step between next and previous values, even though that step sometimes repeats itself, but that repetition is also irregular. I was also trying to reason on how changing d affects output of formula, but my math skiils are clearly not enough.

I am sorry if my language is more of a programmer then mathematician, since I mostly not aware of correct mathematics terms.

Thank you.