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Find smallest positive integer moduls 5 to which

written 7.3 years ago by teamques10 ★ 70k

modified 6.1 years ago by parviagrawal100 • 0

$\ 3^2.3^3.3^4.3^{10} is\ congruent$

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engineering mathematics

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1 Answer

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written 7.3 years ago by teamques10 ★ 70k

Since, $\ 3^2$ = 1 (mod 8)

$\ 3^2$ = 3 (mod 8)

$\ 3^4$= $\ {3^2}^2$= $\ 1^2$ (mod 8)

$\ 3^{10}$=$\ {3^2}^5$=$\ 1^5$ (mod 8)

Thus $\ 3^2$.$\ 3^3$.$\ 3^4$.$\ 3^{10}$

=1.3.1.1 (mod 8) = 3 (mod 8)

$\therefore$ The required smallest +ve integer is 3

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