If m * n is even, it can be expressed as m * n = 2 * t, where t is natural number.
Either m or n has to provide factor of 2 for the right side of equation, so it basically means at least one of them has to be even.
m *n (m multiplied by n) would be mn.
The side is MN although it may be denoted by p (lower case).
You use the definition of even numbers which says it is a number of the form 2n for some integer n, and you take two of them, say 2n and 2m and add them and see that you have 2n+2m=2(n+m) and since n and m are integers so is n+m so lets call it p so the sum is 2p and this is even by definition of even numbers
(m - 5)(n - 4)
If M and N represent numbers and are to be multiplied, it doesn't matter if you multiply NM or MN. Just think, 7x8 and 8x7 still = 56.
MN m and 5 are the terms. 5 is the costant
Suppose m and n are integers. Then 2m+1 is an odd number and 2n is an even number.(2m + 1) * 2n = 4mn + 2n = 2*(2mn + 1). Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + 1 is an integer. Thus the product is a multiple of 2: that is, it is even.
mn(n4-m2)mn(n2+m)(n2-m)
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If m, n, and p are three consecutive integers, then one of them must be even. Let's say the even number is m. Since m is even, it is divisible by two, and so can be written as 2*k, where k is some integer. This means that m*n*p = 2*k*n*p. Since we are multiplying the quantity k*n*p by 2, it must be divisible by two, and therefore must be even.
mn - 4m - 5n + 20 = (mn - 5n) - (4m - 20) = n(m - 5) - 4(m - 5) = (m -5)(n - 4)
MN is not an abbreviation for millions.
,m ,mn,mn,nnn,mnm,,mn
m(n + 1)
Suppose x and y are any two elements of the set.Then x = 3m + 1 and y = 3n + 1 for some integers m and n. Then x*y = (3m + 1)*(3n + 1) = 9mn + 3m + 3n + 1 = 3*(3mn + m + n) + 1. Since m and n are integers, mn+ m + n is also an integer = p, say. Then x*y = 3p + 1. That is the set is closed under multiplication.
Suppose x and y are even numbers. Then x = 2m and y = 2n for some integers m and n.x - y = 2m - 2n = 2(m - n) [distributive property of multiplication over addition/subtraction] = 2k where k is an integer [closure of integers over addition/subtraction] Thus x - y is an even integer.
m *n (m multiplied by n) would be mn.