Are these two fields equal

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In summary, the answer to whether two fields have equal job opportunities depends on the specific fields being compared, as some may have similar opportunities while others may have significant differences. Similarly, whether one field is considered more prestigious or lucrative than the other varies based on the specific fields. The education and training required for each field also differs and should be researched. Additionally, job responsibilities and duties may be similar or different between the two fields, and it is important to research this before making a decision. Finally, the demand for each field can vary, and it is crucial to research the job market and demand before choosing a field.
  • #1
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Hey,
Does anyone know how to show that these fields are equal:
[tex]Q(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_k})=Q(\sqrt{p_1}+\sqrt{p_2}+...+\sqrt{p_k})[/tex],
where [tex]p_1,...,p_k[/tex] are distinct primes in Z.

One inclusion is clear to me, but I'm having problems showing they're equal. Thanks!
 
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  • #2
Induction on k, maybe?
 
  • #3
Right...note to self, always remember about induction. Thank you.
(although my solution using induction looks super messy)
 

1. Are these two fields equal in terms of job opportunities?

The answer to this question depends on the specific fields being compared. Some fields may have similar job opportunities, while others may have significant differences. It is important to research the job market and demand for each field before making a decision.

2. Is one field considered more prestigious or lucrative than the other?

Again, this will vary depending on the specific fields being compared. Some fields may be perceived as more prestigious or offer higher salaries, but this is not always the case. It is important to consider personal interests and skills when choosing a field, rather than solely focusing on external perceptions.

3. Do these two fields require similar education or training?

This will depend on the specific fields being compared. Some fields may have similar educational requirements, while others may have vastly different paths to entry. It is important to research the necessary education and training for each field before making a decision.

4. Are the job responsibilities and duties similar in these two fields?

Again, this will vary depending on the specific fields being compared. Some fields may have overlapping job responsibilities, while others may have completely different duties. It is important to research the day-to-day tasks and responsibilities of each field before making a decision.

5. Is one field in higher demand than the other?

This will depend on the current job market and demand for each field. Some fields may be experiencing a higher demand for workers, while others may be more saturated. It is important to research the job market and demand for each field before making a decision.

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