find 40^(71) mod 437. thanks its 67 but how?


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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
	$40^(25) ≡14 (mod 437) (40^(25) )^3 ≡14^3 ≡122 (mod 437) 40^(75) ≡122 (mod 437) { ((40^(75) ≡122 (mod 437))),((40^4 ≡54(mod 437))) :} { ((40^(75) ≡122+437(8)=3618 (mod 437)...(i))),((40^4 ≡54(mod 437).........(ii))) :} (i)/(ii): 40^(71) ≡67$
	$40^{25} \equiv 14 (m o d 437)$ ${(40^{25})}^{3} \equiv 14^{3} \equiv 122 (m o d 437)$ $40^{75} \equiv 122 (m o d 437)$ ${\begin{cases} 40^{75} \equiv 122 (m o d 437) \\ 40^{4} \equiv 54 (m o d 437) \end{cases}$ ${\begin{cases} 40^{75} \equiv 122 + 437 (8) = 3618 (m o d 437) . . . (i) \\ 40^{4} \equiv 54 (m o d 437) . . . . . . . . . (i i) \end{cases}$ $(i) / (i i) : 40^{71} \equiv 67$
	Answered by lmcp1203 last updated on 25/Jul/24

	$t h a n k s s i r$
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