The Fundamental Theorem of Arithmetic states that if n 1 is an integer then e1e2 n = = P₁¹p²/² ek where P₁, P2, . . . , PÅ are prime and E₁, E2, . . .‚ Ek are positive integers. (Also this decomposition is unique, up to rearrangement of the factors.) Use the formula Pk ..., Pk Suppose n = 7000873. List the primes P₁, P2, as in the theorem. (Please answer as a comma separated list of values, with the primes in *increasing order*.) List the exponents, €₁, €2, . . . , e as in the theorem. (Please answer as a comma separated list of values where the position of the exponent corresponds to the position of the relevant prime in the previous answer.) to compute (n). p(n) = II (p - p²-¹) i=1
The Fundamental Theorem of Arithmetic states that if n 1 is an integer then e1e2 n = = P₁¹p²/² ek where P₁, P2, . . . , PÅ are prime and E₁, E2, . . .‚ Ek are positive integers. (Also this decomposition is unique, up to rearrangement of the factors.) Use the formula Pk ..., Pk Suppose n = 7000873. List the primes P₁, P2, as in the theorem. (Please answer as a comma separated list of values, with the primes in *increasing order*.) List the exponents, €₁, €2, . . . , e as in the theorem. (Please answer as a comma separated list of values where the position of the exponent corresponds to the position of the relevant prime in the previous answer.) to compute (n). p(n) = II (p - p²-¹) i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The Fundamental Theorem of Arithmetic states
that if n > 1 is an integer then
e1e2
n = = P₁¹p²/²
ek
where P₁, P2, . . . ‚ PÅ are prime and E₁, E2, . . .‚ Ek are
positive integers. (Also this decomposition is unique, up
to rearrangement of the factors.)
Use the formula
Pk
····, Pk
Suppose n = 7000873. List the primes P₁, P2,
as in the theorem. (Please answer as a comma
separated list of values, with the primes in *increasing
order*.)
List the exponents, E₁, E2, . . . , Ek as in the theorem.
(Please answer as a comma separated list of values
where the position of the exponent corresponds to the
position of the relevant prime in the previous answer.)
to compute (n).
(n) = II (p - p²-¹)
i=1
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