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Find smallest positive integer moduls 5 to which
written 5.3 years ago by | modified 4.1 years ago by |
$\ 3^2.3^3.3^4.3^{10} is\ congruent$
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written 5.3 years ago by | modified 4.1 years ago by |
$\ 3^2.3^3.3^4.3^{10} is\ congruent$
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written 5.3 years ago by |
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