You are using the new UI (Beta).Return to the original UI

This page has been automatically translated by machine translation. Please note that translations may not be entirely accurate.

keisanHigh-precision calculations for everyday life and work
Login|Register

Search using two "remainders"

Author: shiroeExecutions: 20
TOP/Shared Formulas (Math)/General Math

※ This library was created by a member. This site is not responsible for its content.

Manage Bookmarks
When a natural number n is greater than two distinct natural numbers a and b,
we investigate the largest and smallest natural numbers such that
when divided by a, the remainder is Ra,
and when divided by b, the remainder is Rb.
We will examine the natural numbers within the range of n, but when n is less than or equal to a or b, we will treat the remainder as 0.
Let n0 be the smallest natural number defining the range.
Let n1 be the largest natural number defining the range.
Count the number of natural numbers in the range from n0 to n1 that are coprime to n, and output that count.
a
　　(Divide n by a)
ra
　　(remainder when n is divided by a)
b
　　(Divide n by b)
rb
　　(remainder when n is divided by b)
n0
　　(Minimum scope of investigation)
n1
　　(Maximum scope of the search)
a 　　(Divide n by a)
ra 　　(remainder when n is divided by a)
b 　　(Divide n by b)
rb 　　(remainder when n is divided by b)
n0 　　(Minimum scope of investigation)
n1 　　(Maximum scope of the search)
count 　　(Number of ns that satisfy the condition)
The smallest n that satisfies the condition 
The largest n that satisfies the conditions 
Digit display setting: 50 digits. Fixed digits. Real number calculation mode.
n0 ≤ n1

No customer feedback for this calculation yet.