6:44. Just a minor point: It is incorrect to say that two numbers have to be integers for their product to be integer. For example, 4*3/2 or 8/3 * 3/2 are integers. Since, all the coefficients are integers, so integral variable will only produce integral value for the remaining polynomial. We only need to plugin factors of the constant term for the variable and check the result.
The _Rational Root theorem_ and _Descartes' Rule of Sign_ and _Strum's theorem_ are useful to find real roots and how many there are. Also, if the coefficients of the polynomial in standard form add to zero, the x = 1 is a solution 😁.
1) Love this channel! Subscribed :D 2) At 7:00, couldn’t we make it even easier? If “x” and “-2x^6 + 8x^2” have to be integers, then don’t “x^3” and “-2x^4 + 8” also have to be integers? The only cubic factors of 15 are +1 and -1, so that’s only 2 possibilities to plug into -2x^4 + 8
can someone please explain me, why in the last example, the constant term of -6 wasn’t moved to the right hand side while the earlier example, the constant term was moved. I got confused because the result may be different if it’s moved (the constant term will become positive so there will be only positive divisors and factoring out another x will reduce the power of every terms by x). Thanks in advance
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Wow. That was the simplest explanation of this subclass of diophantane equations I've ever heard.
good
This channel is so underrated. RUclips algo needs a factory reset.
Yes! Number theory is back!
yep
6:44. Just a minor point: It is incorrect to say that two numbers have to be integers for their product to be integer. For example, 4*3/2 or 8/3 * 3/2 are integers. Since, all the coefficients are integers, so integral variable will only produce integral value for the remaining polynomial. We only need to plugin factors of the constant term for the variable and check the result.
Ooh! Ooh! Use Diophantine equations to balance a chemical reaction.
yeah
Excellent explanation. Quick to learn. 👍👍
The _Rational Root theorem_ and _Descartes' Rule of Sign_ and _Strum's theorem_ are useful to find real roots and how many there are. Also, if the coefficients of the polynomial in standard form add to zero, the x = 1 is a solution 😁.
wow.nice
1) Love this channel! Subscribed :D
2) At 7:00, couldn’t we make it even easier? If “x” and “-2x^6 + 8x^2” have to be integers, then don’t “x^3” and “-2x^4 + 8” also have to be integers? The only cubic factors of 15 are +1 and -1, so that’s only 2 possibilities to plug into -2x^4 + 8
Thank you so much!!
Very helpful! Thanks a lot!
Thank you very much for this.. can you do L-functions?
can someone please explain me, why in the last example, the constant term of -6 wasn’t moved to the right hand side while the earlier example, the constant term was moved. I got confused because the result may be different if it’s moved (the constant term will become positive so there will be only positive divisors and factoring out another x will reduce the power of every terms by x). Thanks in advance
Your video always teach me much.
yep it does
We miss Liliana!
At the end shouldn't we be finding all the divisors for 6 cause after going to right -6 will become 6 ??
anyways we get the same divisors (both positive and negative). eg: 1 x 6 and -1 x -6 for positive or -1 x 6 and 1 x -6 for negative
I love it when humans make it easy . is almost 1 2 3 laws
Now do two variables :)
Video incrivel
WOAHHHHHHHHHH!!!!
Sides i and 1 of a right angle triangle. Hypotenus is 0 😁.
Everything is possible in imagination.
Python kickstart?
They are in the process of filming. There were delays because of travel and other imposed restrictions.
yep
Nifty
I can't even say diophantine without getting a tongue-twist.
lol
Primero
Hello ma'am after long time
Is everything ok
yep