Difference between revisions of "Jyotiraditya Jadhav"
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<math>\measuredangle = \cos^-1 [{a^2+b^2-c^2}(2ab)^-1] </math> | <math>\measuredangle = \cos^-1 [{a^2+b^2-c^2}(2ab)^-1] </math> | ||
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| + | '''[[Jadhav Prime Quadratic Theorem]]''' | ||
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| + | It states that if a [https://en.wikipedia.org/wiki/Quadratic_equation Quadratic Equation] <math>ax^2+bx+c </math> is divided by <math>x</math> then it gives the answer as an '''[https://en.wikipedia.org/wiki/Integer Integer]''' if and only if <math>x </math> is equal to 1, [https://en.wikipedia.org/wiki/Integer_factorization Prime Factors] and [https://en.wikipedia.org/wiki/Composite_number composite] [https://en.wikipedia.org/wiki/Divisor divisor] of the constant <math>c</math> . | ||
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| + | Let the set of [https://en.wikipedia.org/wiki/Integer_factorization prime factors] of constant term <math>c </math> be represented as <math>p.f.[c] </math> and the set of all [https://en.wikipedia.org/wiki/Composite_number composite] [https://en.wikipedia.org/wiki/Divisor divisor] of <math>c </math> be <math>d[c] </math> | ||
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| + | <math>\frac{ax^2+bx+c}{x} \in Z </math> Iff <math>x \in </math> <math>p.f.[c] \bigcup d[c] \bigcup {1} </math> where <math>a,b,c \in Z </math>. | ||
Revision as of 06:19, 21 July 2021
Jyotiraditya Jadhav is an India-born Mathematician and a mathematical researcher, who was titled "Mathematician" by Proof Wiki after publication of his impact-full formula, Jadhav Theorem.
Researches
If any three consecutive numbers are taken say a,b and c with a constant common difference, then the difference between the square of the 2nd term (b) and the product of the first and the third term (ac) will always be the square of the common difference (d).
Representation of statement in variable :
In any isosceles triangle let the length of equal sides be "s" and the angle formed between both the sides be . then the area of the complete triangle can be found by Jadhav Isosceles Formula as below:
![$[{sin (\theta/2)}{cos( \theta /2)}{s^2}]$](http://latex.artofproblemsolving.com/d/8/1/d813e6ba16795f3dacc4580cfcce411d2cba3f67.png)
In an incomplete division process if the dividend is lesser then Divisor into product of 10 raise to a power "k", and bigger then divisor into product of 10 with power "k-1" then there will be k number of terms before decimal point in an divisional process.
Jadhav Triads are groups of any 3 consecutive numbers which follow a pattern , was discovered by Jyotiraditya Jadhav and was named after him.
Jadhav Angular Formula evaluates the angle between any two sides of any triangle given length of all the sides.
![$\measuredangle = \cos^-1 [{a^2+b^2-c^2}(2ab)^-1]$](http://latex.artofproblemsolving.com/0/1/e/01e82f79523bae6e9821215c12400fd36962e308.png)
Jadhav Prime Quadratic Theorem
It states that if a Quadratic Equation 
is divided by 
then it gives the answer as an Integer if and only if is equal to 1, Prime Factors and composite divisor of the constant 
.
Let the set of prime factors of constant term be represented as ![$p.f.[c]$](http://latex.artofproblemsolving.com/2/4/f/24f7db09513a1d0a18bbce3552e7378d9f3d9c7e.png)
and the set of all composite divisor of be ![$d[c]$](http://latex.artofproblemsolving.com/c/1/9/c19da214f0c45b9871099584d4d1264429895702.png)
Iff 
![$p.f.[c] \bigcup d[c] \bigcup {1}$](http://latex.artofproblemsolving.com/d/8/6/d86c886ce3ea5c8fc234dd32921f883078a728f7.png)
where 
.
