Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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What are the philosophers paid for?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,302

For one thing they can head over to a university and find teaching jobs or author a book.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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It looks like they are teaching each other expressions.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,302

They are both going Hmmm.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**zetafunc.****Guest**

bob bundy wrote:

To extract a contradiction argument you would have to assume that x + y ≠ 88 and show this leads to a contradiction. Since many other values (other than 88) are possible, I think you'd have a tough time with this.

Bob

It might be doable -- I haven't tried via contradiction, although I'd assume you'd start with *x + y < 88* and find bounds for *a + b + ab* that don't include 2020, then do something similar for the case *x + y > 88*. The AM-GM inequality might help for this due to the ab term. However, the problem seems engineered to make use of the factorisation *(a + 1)(b + 1) - 1* = *a + b + ab*.