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# Monthly Archives: August 2018

## Efficiency of repeated squaring

As you probably realized if you read both, my recent post without words connects directly to my previous post on exponentiation by repeated squaring Each section shows the sequence of operations used by the repeated squaring algorithm to build up … Continue reading

Posted in computation
Tagged binary, double, efficiency, exponent, increment, repeated, squaring, steps
7 Comments

## Modular exponentiation by repeated squaring

In my last post we saw how to quickly compute powers of the form by repeatedly squaring: ; then ; and so on. This is much more efficient than computing powers by repeated multiplication: for example, we need only three … Continue reading

Posted in computation, number theory
Tagged algorithm, exponentiation, logarithmic, modular, primality, repeated, squaring, test
4 Comments

## Modular exponentiation

In my previous post I explained the Fermat primality test: Input: Repeat times: Randomly choose . If , stop and output COMPOSITE. Output PROBABLY PRIME. In future posts I’ll discuss how well this works, things to worry about, and so … Continue reading

## The wizard’s rational puzzle (mind your p’s and q’s!)

You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozy-looking room, with a hardwood floor, a few exotic-looking rugs, and wood paneling on the walls. He … Continue reading

Posted in arithmetic, challenges, logic, programming, puzzles
Tagged arithmetic, denominator, numerator, puzzle, rational, wizard
15 Comments

## The Fermat primality test

After several long tangents writing about orthogons and the chromatic number of the plane, I’m finally getting back to writing about primality testing. All along in this series, my ultimate goal has been to present some general primality testing algorithms … Continue reading