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#1 Re: Euler Avenue » A proof of the Riemann hypothesis » 2018-09-24 08:33:09

Sir Michael Francis Atiyah … is a British-Lebanese mathematician specialising in geometry.

Wikipedia


At a hotly-anticipated talk at the Heidelberg Laureate Forum today [Monday 24 September 2018], retired mathematician Michael Atiyah delivered what he claimed was a proof of the Riemann hypothesis, a challenge that has eluded his peers for nearly 160 years.

New Scientist

#5 Re: Puzzles and Games » Playing with natural numbers and SQRT » 2018-08-10 05:18:54

If a = 2, b = 1, c = 4, then A = √(2+1·√ 4) = 2, B = √(2−1·√ 4) = 0, S = A + B = 2 ≠ b.

#6 Re: Help Me ! » Inductive and Deductive Reasoning » 2018-07-31 00:25:10

bob bundy wrote:

Draw three distinct, parallel lines and another line (a transversal) to cross them all.

But those three lines may not be in one and the same plane.

#7 Re: Help Me ! » Conditional Statements and Venn Diagrams » 2018-07-28 16:11:31

Let x be the number of people enrolled in all three classes. Then:

  1. 170−x are enrolled in art and drama but not piano,

  2. 150−x are enrolled in drama and piano but not art,

  3. 300−x are enrolled in piano and art but not drama.

Now that you have split the numbers into non-overlapping groups, you can add them up:

#8 Re: Help Me ! » Find all real solutions: Proof help » 2018-07-28 02:29:13

Let us apply zetafunc’s method in another way. Dividing by 2 and rearranging gives

Now consider the following table:

Thus we see that outside of {0,±1} the equation has no solution as the LHS and RHS have opposite signs. This proves that there are no solutions other than x = 0, ±1.

#9 Re: Help Me ! » Find all real solutions: Proof help » 2018-07-26 23:44:22

There are precisely three solutions:

Unfortunately I do not know how to prove it rigorously. Maybe Bob Bundy can come up with more helpful information.

#10 Re: Formulas » Tests For Divisibility » 2018-07-24 10:21:40

Here’s a YouTube video on tests of divisibility and how to apply them to some math problems.

I found the solution to finding all palindromic four-digit powers particularly interesting.

#11 Re: Help Me ! » A cubic eq. » 2018-07-24 06:09:34

anonimnystefy wrote:

Can you help me solve this equation?

#12 Re: Exercises » Mathematical Induction » 2018-07-15 20:35:17

What do you mean by why is n term not 2n−1?

Since the thread title is mathematical induction, I take it you want to prove the formula for the sum of the first n odd positive integers. To do this, you need to know what the formula is in the first place. If you’re not given the formula, you can make a guess and then proceed to prove it. So, trying the first few sums …

I think you can make a guess as to what the formula is going to be.

#13 Re: Exercises » Quadratic » 2018-07-15 00:12:13

I presume ɑ and β are the roots, which are complex. Since we are going to deal with their powers, best to convert them to cos–sin form:

So the roots are

one of them is ɑ, the other is β. Since the question doesn’t say which is which, you may as well take your pick. Now use De Moivre’s theorem.

#15 Re: Help Me ! » Division » 2018-07-04 21:59:22

Do the long division yourself!

#16 Re: Puzzles and Games » [ASK] Exact Measure Using 2 Bottles » 2018-07-04 20:35:26

By the way, this thread is better in the Puzzles and Games section.

#17 Re: Help Me ! » Division » 2018-07-04 20:28:34

Zeeshan 01 wrote:

Do that division, given in https://www.mathsisfun.com/long_division.html

Alg Num Theory wrote:

I’m not doing your homework for you. You do it yourself.

#18 Re: Help Me ! » Division » 2018-07-03 10:14:23

In problems like this, the first thing to is to reduce the fraction to its lowest terms:

so you’ll be doing the following long division:

If the denominator ends with one or more 0, you can shift the decimal point in the numerator to get rid of the 0:

giving

#19 Re: Help Me ! » Division » 2018-07-02 08:55:25

I’m not doing your homework for you. You do it yourself.

#20 Re: Help Me ! » Division » 2018-07-02 05:19:07

Go on, then. Use long division.

#24 Re: Jokes » Country jokes » 2018-06-17 17:30:58

Q: Why is the Northeast of England is so old and broken down?
A: Because it has aged with Tyne and is now the worse for Wear!

#25 Re: Help Me ! » Sequences » 2018-06-16 23:11:58

Bob, I think r=0 is also possible for (a).

For (b), I think the answer is all nonnegative integers. Clearly there are infinite geometric sequences with no integers, e.g.

If r = 1, add 1 as the first term to the above sequence.

If r > 1, then

is an infinite geometric sequence (common ratio 1/r) with exactly r integer terms (the first r of them).

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