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Math Help - Order of an element

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    Order of an element

    Suppose that gcd(a,n)=1, m|n, then order of a in m divides order of a in n.
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    Quote Originally Posted by tttcomrader View Post
    Suppose that gcd(a,n)=1, m|n, then order of a in m divides order of a in n.
    Let k be order of a mod m and r be order of a mod n. Then it means a^k\equiv 1(\bmod m) and a^r\equiv 1(\bmod n). But since m|n it means a^r\equiv 1(\bmod m). Since k is the order mod m it means k|r.
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