To find: The smallest positive integer that solves the congruencesx\equiv 3(\bmod 7), x\equiv 4(\bmod 5)

banganX

banganX

Answered question

2021-02-21

To find: The smallest positive integer that solves the congruences
x3(b mod 7),x4(b mod 5)

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-02-23Added 95 answers

Given information:
The congruences x3(b mod 7),x4(b mod 5)
Consider the given congruences
x3(b mod 7),x4(b mod 5)
‘The congruence x3(b mod 7) means if x is divided by 7, the remainder is 3.
So the number x is one of the numbers in the following list:
3, 10, 17, 24, 31, 38, 45, -
Similarly, the congruence x4(b mod 5) means if x is divided by 5, the remainder is 4.
So the number x is one of the numbers in the following list:
4,9, 14, 19,24, 29,34, 39, 44, -
The smallest number that is found in both the lists is 24, so the
smallest number that solves the congruences
x3(b mod 7),x4(b mod 5) is 24.
x=24
Final Statement:
The smallest positive integer that solves the congruences
x3(b mod 7),x4(b mod 5) is x = 24.

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