X-Nico

3 unusual facts about modulo

Modulo

Modular arithmetic: Part of a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus.

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Módulo, a Brazilian company specializing in IT governance

Módulo

Módulo is a Brazilian company with international operations specializing in technology for Governance, Risk and Compliance.

However, one can combine these remainders recursively to reduce the cost, using the following trick: if we want to evaluate $x(z)$ modulo two polynomials $U(z)$ and $V(z)$ , we can first take the remainder modulo their product $U(z)$ $V(z)$ , which reduces the degree of the polynomial $x(z)$ and makes subsequent modulo operations less computationally expensive.

Discrete logarithm records

On 18 Jun 2005, Antoine Joux and Reynald Lercier announced the computation of a discrete logarithm modulo a 130-digit (431-bit) strong prime in three weeks, using a 1.15 GHz 16-processor HP AlphaServer GS1280 computer and a number field sieve algorithm.

Ducci sequence

The linear map in modulo 2 can further be identified as the cellular automata denoted as rule 102 in Wolfram code and related to rule 90 through the Martin-Odlyzko-Wolfram map.

Hex dump

When hex dumps are intended to be manually entered into a computer, such as was the case with print magazine articles of home computer era a checksum byte (or two) would be added at the end of each row, commonly calculated as simple 256 modulo of sum of all values in the row or a more sophisticated CRC.

Link aggregation

;XOR (balance-xor): Transmit network packets based on (source MAC address XOR'd with destination MAC address) modulo NIC slave count.

MSI Barcode

There are two modulo 11 algorithms which use different repeated weighting factor patterns: the IBM algorithm which uses (2,3,4,5,6,7), and the NCR algorithm which uses (2,3,4,5,6,7,8,9).

Rado graph

Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.