find-40-71-mod-437-thanks-its-67-but-how-

Question Number 209892 by lmcp1203 last updated on 25/Jul/24

f i n d 40^{71} m o d 437 . t h a n k s

i t s 67 b u t h o w ?

Answered by Rasheed.Sindhi last updated on 25/Jul/24

40^{25} \equiv 14 (m o d 437)

{(40^{25})}^{3} \equiv 14^{3} \equiv 122 (m o d 437)

40^{75} \equiv 122 (m o d 437)

{\begin{cases} 40^{75} \equiv 122 (m o d 437) \\ 40^{4} \equiv 54 (m o d 437) \end{cases}

{\begin{cases} 40^{75} \equiv 122 + 437 (8) = 3618 (m o d 437) \dots (i) \\ 40^{4} \equiv 54 (m o d 437) \dots \dots \dots (i i) \end{cases}

(i) / (i i) : 40^{71} \equiv 67

Answered by lmcp1203 last updated on 25/Jul/24

t h a n k s s i r

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