Question

15x ≡ 25(mod 35) എന്ന congruence ന്ടെ പരിഹാരങ്ങൾ ഏത് ?

• A. 4 , 11, 18, 25, 32
• B. 4 , 1, 8, 25, 39
• C. 2 , 16, 18, 25, 32
• D. 2 , 4, 8, 15, 32

Answer 1

Answer:

A. 4 , 11, 18, 25, 32

$15 ≡ 25 (mod 35)$

$a=15 ;; b = 25 ;; m= 35$

$d= (15, 35) = 5$

5 | 25 => 5 solutions

$\frac{15}{5}x≡\frac{25}{5}(mod \frac{35}{5})$

=> 3x ≡ 5(mod 7)

t=x=4 => t, t+ \frac{m}{d}, t+\frac{2m}{d} + t+\frac{3m}{d} +...... t+\frac{(d-1)m}{d}

t=4;

solutions

$4, 4+7 , 4 + 2 \times 7 + 4 + 3 \times 7 + 4 + 4 \times 7$

$= 4 , 11, 18, 25, 32$