1. Math
  2. Advanced Math
  3. if a and b are represented by 16 what conditions...

Question: if a and b are represented by 16 what conditions...

Question details

If a and b are represented by (1.6), what conditions must be satisfied by the exponents if a is to be a cube? Also, what about gcd (a^2,b^2)?

In the application of the fundamental theorem we frequently write any integer a > 1 in the form where α(p) is a non-negative integer, and it is understood that α(p) 0 for all sufficiently large primes p. If a-1 then α(p)-0 for all primes p, and the product may be considered to be empty. For brevity we sometimes write a-Πp®, with the tacit understanding that the exponents α depend on p and, of course on a. If and ab-c, then α(p)+β(p) y(p) for all p, by the fundamental theorem. Here ale, and we note that α(p) < γ(p) for all p. If, conversely, a(p) < γ(p) for all p, then we may define an integer b-11pA) with B(p)y(p) - a(p). Then ab-c, which is to say that alc. Thus we see that the divisibility relation a|c is equivalent to the family of inequalities a(p)<y(p). As a consequence, the greatest common divisor and the least common multiple can be written as

I asked the same question a few minutes ago but posted the wrong equation so please do not copy that answer.

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution