Ask Dr. Math 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?