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| − | In Mathematics, '''Jadhav's Prime Quadratic Theorem''' is based on '''[https://en.wikipedia.org/wiki/Algebra Algebra]''' and '''[https://en.wikipedia.org/wiki/Number_theory Number Theory]'''. Discovered by an Indian Mathematician '''[[Jyotiraditya Jadhav]]'''. Stating a condition over the value of <math>x </math> in the [https://en.wikipedia.org/wiki/Quadratic_equation quadratic equation] <math>ax^2+bx+c </math>.
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| − | == 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>.
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| − | == Historical Note ==
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| − | [https://proofwiki.org/wiki/Mathematician:Jyotiraditya_Jadhav Jyotiraditya Jadhav] is a school-student and is always curious about [https://www.ck12.org/book/ck-12-middle-school-math-concepts-grade-7/section/1.2/#:~:text=A%20numerical%20pattern%20is%20a,you%20to%20extend%20the%20pattern. numerical patterns] which fall under the branch of [https://en.wikipedia.org/wiki/Number_theory Number Theory]. He formulated many [https://en.wikipedia.org/wiki/Arithmetic arithmetic based equations] before too like [https://proofwiki.org/wiki/Jadhav_Theorem Jadhav Theorem], [https://en.everybodywiki.com/Jadhav_Triads Jadhav Triads], [[Jadhav Arithmetic Merging Equation]] and many more. While he was solving a question relating to [https://en.wikipedia.org/wiki/Quadratic_equation Quadratic Equations] he found out this numerical pattern and organized the [https://en.wikipedia.org/wiki/Theorem theorem] over it.
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| − | == Proving "Jadhav Prime Quadratic Theorem" ==
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| − | Now let us take <math>\frac{ax^2+bx+c}{x} </math> written as <math>\frac{x[ax+b]+c}{x} </math>
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| − | To cancel out <math>x </math> from the denominator we need <math>x </math> in numerator and to take <math>x </math> as common from whole quadratic equation we need to have <math>c </math> as a composite number made up as prime-factors with at least one factor as <math>x </math> or in other words <math>c </math> should be a multiple of <math>x </math> and hence telling us <math>x </math> should at least be a prime factor, composite divisor or 1 to give the answer as an Integer.
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| − | Hence Proving Jadhav Prime Quadratic Theorem.
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| − | '''Original Research paper''' can be found [https://issuu.com/jyotiraditya123/docs/jadhav_prime_quadratic_theorem here on Issuu]
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| − | __INDEX__
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