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- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/03%3A_Proof_Techniques_I/3.06%3A_Proofs_and_Disproofs_of_Existential_StatementsFrom a certain point of view, there is no need for the current section. If we are proving an existential statement we are disproving some universal statement. (Which has already been discussed.) Simil...From a certain point of view, there is no need for the current section. If we are proving an existential statement we are disproving some universal statement. (Which has already been discussed.) Similarly, if we are trying to disprove an existential statement, then we are actually proving a related universal statement. Nevertheless, sometimes the way a theorem is stated emphasizes the existence question over the corresponding universal.
- https://math.libretexts.org/Courses/Coalinga_College/Math_for_Educators_(MATH_010A_and_010B_CID120)/04%3A_Number_Theory/4.05%3A_Factors_and_GCFFactors are numbers that divide evenly into another number without a remainder. The Greatest Common Factor (GCF) is the largest positive integer that divides two or more numbers without a remainder, w...Factors are numbers that divide evenly into another number without a remainder. The Greatest Common Factor (GCF) is the largest positive integer that divides two or more numbers without a remainder, with applications in simplifying fractions and algebraic expressions. Methods for finding factors and calculating the GCF include listing factors, prime factorization, and the Euclidean algorithm.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/01%3A_Introduction_and_Notation/1.05%3A_Some_Algorithms_of_Elementary_Number_TheoryAn algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th...An algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th and 9th centuries A.D. He is remembered for his algebra treatise Hisab al-jabr w’al-muqabala from which we derive the very word “algebra,” and a text on the Hindu-Arabic numeration scheme.