x-Z-15-48a-1-x-mod-17-find-x-

Question Number 144961 by mathdanisur last updated on 30/Jun/21

x \in Z^{+}

15^{48 a + 1} \equiv x (m o d 17) f i n d x = ?

Answered by Rasheed.Sindhi last updated on 01/Jul/21

15^{8} \equiv x (m o d 17)

15^{8} \equiv 1 (m o d 17)

{(15^{8})}^{6 a} \equiv {(1)}^{6 a} (m o d 17)

15^{48 a} \equiv 1

15^{48 a} . 15 \equiv 1.15 (m o d 17)

15^{48 a + 1} \equiv 15 (m o d 17)

x \equiv 15 (m o d 17)

x = 15 + 17 k; k \in {0, 1, 2, \dots .}

Commented by mathdanisur last updated on 01/Jul/21

c o o l S i r t h a n k y o u, a n s w e r x = 15 ?

Commented by Rasheed.Sindhi last updated on 01/Jul/21

15 + 17 k; W h e r e k \in {0, 1, 2, \dots}

Commented by mathdanisur last updated on 01/Jul/21

S i r, b u t a n s w e r : 15

Commented by Rasheed.Sindhi last updated on 01/Jul/21

T h e l e a s t p o s i t i v e i n t e g r a l v a l u e

o f x i s 15

Commented by mathdanisur last updated on 01/Jul/21

t h a n k s S i r