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What is Mod?

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What is Mod?, a selection of answers from the Dr. Math archives.

Mod
What does the term 'mod' mean?

What is Modulus?
I have used the mod command and know what the results mean, but I don't understand the theory behind it and what is actually happening.

Modulus Operator Problem
Can you explain this problem to me? 4 mod 3 = ?

Mod, Modulus, Modular Arithmetic
What does 'mod' mean?

Casting Out Nines and Elevens
Why is nine used in proving this math answer?

Modular Arithmetic
For any integer a, a^4 is congruent to 0 or 1 (mod 5)... We were able to work with the odd number case so it is just the even case that is getting us stuck.

Proof Involving mod 5
Prove n^2 mod 5 = 1 or 4 when n is an integer not divisible by 5.

Computing a^((N-1)/2) mod N
Is there a shortcut for doing a^((n-1)/2) mod N?

Division of Large Numbers
What is the remainder when 7^100 is divided by 13? Give a general strategy and an explanation.

Using Mod to Find Digits in Large Numbers
Find the last two digits in 1996^1996.

Finding 13^99
What is the units digit of 13 to the 99th power?

Find the Monster Mod 11, Mod 2310
Find an integer n between 0 and 2309 with the property that 10^10^10^34 = n (mod 2310).

Numbers in the Fibonacci Sequence
How can I show that there is a number in the Fibonacci sequence that ends in 999999999999? For what numbers n is there a number in the Fibonacci sequence that ends in n of 9?

Mod Function and Negative Numbers
What is the correct value for the function MOD(-340,60)? Microsoft Excel returns the value 20, while Lotus 1-2-3 returns the value -40. Can you explain the difference?

Euler's theorem
How do I find the inverse of a modulo m using Euler's theorem?

Reverse Modulus Operator
Is there an operator that would return 2 when we we do 6 * 0, * being this new operator?

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