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In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect ...
The questions on STEP 2 and 3 were about the same difficulty. Both STEP 2 and STEP 3 are harder than STEP 1. [6] For the 2019 examinations onwards, the specifications have been updated to reflect the reforms in A Level Mathematics and Further Mathematics; [7] in addition, the number of questions in each paper has been reduced. Specifically:
So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [ 2 ] [ 4 ] There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers, but it is unknown whether there exist odd perfect numbers.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k , a number n is called k -perfect (or k -fold perfect) if the sum of all positive divisors of n (the divisor function , σ ( n )) is equal to kn ; a number is thus perfect if and ...
The Euclid–Euler theorem states that an even natural number is perfect if and only if it has the form 2 p−1 M p, where M p is a Mersenne prime. [1] The perfect number 6 comes from p = 2 in this way, as 2 2−1 M 2 = 2 × 3 = 6, and the Mersenne prime 7 corresponds in the same way to the perfect number 28.
Paper 1 is a multiple choice paper and consists of forty questions, all have a one-point score value. Paper 2 is the subjective area of Maths. There are 15 questions here in total, the first five questions have a three-point score value, questions 6-10 have a four-point score value, and the last five have a five-point score value.
The examination consists of multiple-choice and written questions, and Continuous (Internal) Assessment marks provided by the schools. In Ghana, candidates are graded on a nine-point scale, with Grade 1 for highest performance and Grade 9 for lowest. [5] From 2017–Date, Candidates in Nigeria have been graded on a non-linear 5 point scale from
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