#### English Title

Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders

#### Enestrom Number

36

#### Fuss Index

12

#### Original Language

Latin

#### English Summaries

Euler proves the Chinese Remainder Theorem by constructing an algorithm to find the smallest number which, divided by given numbers, leaves given remainders. He begins by solving the case in which two relatively prime divisors with corresponding remainders are given and proposes that by repeating his algorithm, he can solve similar problems with any number of constraints. Euler then discusses scenarios in which divisors are not relatively prime, and ends the paper with an application of his algorithm to a classic problem: dating events in Roman indictions.

#### Published as

Journal article

#### Published Date

1740

#### Written Date

1740

#### Content Summary

Euler proves the Chinese remainder theorem by constructing an algorithm to find the smallest number which, divided by given numbers, leaves given remainders. He begins by solving the case in which two relatively prime divisors with corresponding remainders are given and proposes that by repeating his algorithm, he can solve similar problems with any number of constraints. Euler then discusses scenarios in which divisors are not relatively prime, and ends the paper with an application of his algorithm to a classic problem: dating events from their Roman indictions.

#### Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 7, pp. 46-66.

#### Opera Omnia Citation

Series 1, Volume 2, pp.18-32.

#### Record Created

2018-09-25