MATLAB: Possible to mod a number in the middle of a cycle

cycleerrorexponentsmodmodulusoffproblemround

Here is a portion of my code I need help with:
for m = 1:k    
for j = 1:FEE
     number = m.^j;
  if number >= 10000000
     number = mod(number,k);
  else
  end
To illustrate my problem, lets look at a specific example.
Lets say m = 9, we want to look at when j = 9, 18
9^9 is okay because you get no round off error, 9^18 on the other hand gives round off error.
Is there a way to run 9^any power and mod it when it exceeds the limit 10000000 at any point?
I feel like in this portion of my code matlab is running 9^18 for example, noticing it exceeds 10000000 then modding (9^18 first, then modding would result in round off error right?), I want matlab to run 9*9…* 9 and mod it every single time it exceeds 1000000 before finishing the multiplication.

Best Answer

You're performing modular exponentiation. There are plenty of fast algorithms around that do not involve ever calculating the exponentiation first (it's an important part of cryptography), including on the wiki page linked or on the file exchange.
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