Solve the following linear congruence, 25x \equiv 15(\bmod 29)

floymdiT

floymdiT

Answered question

2021-05-09

Solve the following linear congruence,
25x15(bmod29)

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-05-11Added 107 answers

Step 1 
The equation for linear congruence provided is 
25x15(bmod29) 
Here, a=25, b=15, m=29, 
And, 
gcd(a,m)=gcd(25,29)=1 
Therefore, there is only one incongruent solution to the congruence, which can be found by solving the corresponding Diophantine equation.
ax+by=m25x+15y=29 
Step 2 
Let us check the value of x=11. 
That is, at x =11, 
11×25+15=275+15=290 
which is 0bmod29
Hence x=11 is the solution of given equation.

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