Mathematics OpenStudy (anonymous):

Show that an integer (>1) with prime factors p1^k1p2^k2.....pn^kn is a square if and only if each of the exponents k is even. OpenStudy (anonymous):

one way is easy enough. if $k_i$ are even then this is the square of $p_1^{\frac{k_1}{2}}\cdotp_2^{\frac{k_2}{2}}...\cdot p_n^{\frac{k_n}{2}}$ OpenStudy (anonymous):

Mixing up my letters...:-) OpenStudy (anonymous):

other way pretty straight forward too. if z is a square, then it is the square of something, say m by fundamental theorem of arithmetic $m=p_1^{\alpha_1}\cdot p_2^{\alpha_2}\cdot ...\cdot p_n^{\alpha_n}$ OpenStudy (anonymous):

And the generalization since u seem to be in fine form today...? OpenStudy (anonymous):

so $z=m^2=(p_1^{\alpha_1}\cdot p_2^{\alpha_2}\cdot ...\cdot p_n^{\alpha_n})^2$ etc OpenStudy (anonymous):

one generalization is that $\sqrt[n]{z}$ is irrational unless z is a perfect nth root OpenStudy (anonymous):

lol, that will do... OpenStudy (anonymous):

not the one you wanted i bet OpenStudy (anonymous):

An integer is an nth power ifff each of prime exponents is a multiple of n (for lesse mortals) OpenStudy (anonymous):

yeah so it is the same mutatis mutandis (god but i love fancy latin terms) OpenStudy (anonymous):

U would make a number theorist cry....:-)

Latest Questions nuna: Lesson 9: Language Focus: word choice and voice online practice. English 9 A unit
4 minutes ago 0 Replies 0 Medals KingCrazy: https://questioncove.com/assets/attachments/message-1621296930-60a307226f51e1a409f42400-20210517_201119_Normal.
48 minutes ago 1 Reply 0 Medals giveanswersmeanthelp: Which source would be the best choice to support a research paper on the evolution of baseball in the United States? A.
1 hour ago 1 Reply 0 Medals Ferrari: Read the dialogue and choose the option with the correct adjectives missing in the blanks to complete the sentences.
2 hours ago 3 Replies 1 Medal Ferrari: HELP AAA
2 hours ago 7 Replies 1 Medal babygirl123: any bunny experts one of my bunnys just gave birth to 10 little babys and im not
37 seconds ago 3 Replies 0 Medals nipun: A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire.
15 hours ago 0 Replies 0 Medals nipun: A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire.
15 hours ago 0 Replies 0 Medals lildizzy: the company also discovered that it costs $19.50 to produce 3 calculators,$47.50
16 hours ago 0 Replies 0 Medals Backstabber: hooray i tried pastel drawing for the first time canu2019t wait for the future iu
18 minutes ago 8 Replies 3 Medals