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Let f(x)=x^n+a_(n-1)x^(n-1)+...+a_0 with n>=2 and a_i an integer have a rational root x=p/q.

Consider q^(n-1)f(p/q).

q^(n-1)f(p/q)=p^n/q+a_(n-1)p^(n-1)+...+a_0q^(n-1)=0

==> a_(n...

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Silicon, as there are many covalent bonds which are strong and require a very high energy to be broken.

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We will answer this by considering the numbers which contribute towards trailing zeros and by calculating how many such numbers there are within 100!. The solution should enlighten the student on the use ...