To find: The smallest positive integer that solves the congruences x\equiv 1(\bmod 6), x\equiv 7(\bmod 8)

geduiwelh

geduiwelh

Answered question

2021-05-08

To find: The smallest positive integer that solves the congruences
x1(bmod6),x7(bmod8)

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-05-10Added 102 answers

Given information:
The congruences are x1(bmod6),x7(bmod8).
Consider the given congruences
x1(bmod6),x7(bmod8)
The congruences x1(bmod6) means if x is divided by 6, the remainder is 1.
So number x is one of the numbers in the following list:
7,13,19,25,31,37,43,...
Similarity, the congruence x7(bmod8) means if x is divided by 8, the remainder is 7.
So the number x is one of the numbers in the following list:
7,15,22,29,36,43,49,56,63,...
The smallest number that is found in both the lists is 7, so the smallest number that solves the congruences
x3(bmod7),x4(bmod5) is 7.
x=7.
Final Statement:
The smallest positive integer that solves the congruences
x3(bmod7),x4(bmod5) is x= 7.

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