The natural numbers 23 and 32 are consecutive, namely, 8 and 9. Catalan's conjecture states thatthere are no other examples of consecutive natural numbers representable as powers of naturalnumbers with integer exponents greater than 1.Mark all of the statements that are equivalent to Catalan's conjecture.O (vx e N) (vy e N) (vm e N) (vn e N) (if x = 3 and y = 2 and m = 2 and n = 3, then m > 1 and n> 1 andxm - y = 1)(3x e N) (3y e N) (3m e N) (3n e N) (m > 1 and n > 1 and xm - y = 1 and x + 3 and y + 2 and m + 2 and n = 3)(3x € N) (ay e N) (3m e N) (3n e N) (m > 1 and n> 1 and x" - y" = 1 and (x + 3 or y + 2 or m + 2 or n + 3)O (vx € N) (vy e N) (vm e N) (vn E N) (if m > 1 and n > 1 and x" – y = 1, then x = 3 and y = 2 and m = 2 andn- 3)O (*x € N) (vy € N) (m e N) (vn E N) (if x + 3 or y + 2 or m = 2 or n = 3, then x" - y = 1 or m = 1 or n = 1)

Name: The natural numbers 23 and 32 are consecutive, namely, 8 and 9. Catal
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Description: The natural numbers 23 and 32 are consecutive, namely, 8 and 9. Catalan's conjecture states thatthere are no other examples of consecutive natural numbers representable as powers of naturalnumbers with integer exponents greater than 1.Mark all of th

The conjecture says that, for natural numbers x,y,m and n, xm-yn=1 if and only if x=3, y=2, m=2 and…

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The natural numbers 2° and 32 are consecutive, namely, 8 and 9. Catalan's conjecture states that there are no other examples of consecutive natural numbers representable as powers of natural numbers with integer exponents greater than 1. Mark all of the statements that are equivalent to Catalan's conjecture. O (vx e N) (vy € N) (vm e N) (vn E N) (if x = 3 and y = 2 and m = 2 and n = 3, then m > 1 and n > 1 and x" - y" = 1) ) (3x e N) (3y e N) (3m eN) (an e N) (m > 1 and n > 1 and x" - y^ = 1 and x + 3 and y - 2 and m + 2 and n - 3) (3x € N) (3y e N) (3m e N) (an e N) (m > 1 and n > 1 and x" - y" - 1 and (x * 3 or y 2 or m « 2 or n« 3) O (Yx € N) (vy € N) (vm e N) (vn E N) (if m > 1 and n> 1 and x" - y - 1, then x = 3 and y - 2 and m - 2 and n- 3) O (Yx € N) (vy € N) (vm € N) (vn E N) (if x + 3 or y = 2 or m « 2 or n 3, then x - y + 1 or m = 1 or n = 1)

The natural numbers 2° and 32 are consecutive, namely, 8 and 9. Catalan's conjecture states that there are no other examples of consecutive natural numbers representable as powers of natural numbers with integer exponents greater than 1. Mark all of the statements that are equivalent to Catalan's conjecture. O (vx e N) (vy € N) (vm e N) (vn E N) (if x = 3 and y = 2 and m = 2 and n = 3, then m > 1 and n > 1 and x" - y" = 1) ) (3x e N) (3y e N) (3m eN) (an e N) (m > 1 and n > 1 and x" - y^ = 1 and x + 3 and y - 2 and m + 2 and n - 3) (3x € N) (3y e N) (3m e N) (an e N) (m > 1 and n > 1 and x" - y" - 1 and (x * 3 or y 2 or m « 2 or n« 3) O (Yx € N) (vy € N) (vm e N) (vn E N) (if m > 1 and n> 1 and x" - y - 1, then x = 3 and y - 2 and m - 2 and n- 3) O (Yx € N) (vy € N) (vm € N) (vn E N) (if x + 3 or y = 2 or m « 2 or n 3, then x - y + 1 or m = 1 or n = 1)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic Video

Question

The natural numbers 23 and 32 are consecutive, namely, 8 and 9. Catalan's conjecture states that
there are no other examples of consecutive natural numbers representable as powers of natural
numbers with integer exponents greater than 1.
Mark all of the statements that are equivalent to Catalan's conjecture.
O (vx e N) (vy e N) (vm e N) (vn e N) (if x = 3 and y = 2 and m = 2 and n = 3, then m > 1 and n> 1 and
xm - y = 1)
(3x e N) (3y e N) (3m e N) (3n e N) (m > 1 and n > 1 and xm - y = 1 and x + 3 and y + 2 and m + 2 and n = 3)
(3x € N) (ay e N) (3m e N) (3n e N) (m > 1 and n> 1 and x" - y" = 1 and (x + 3 or y + 2 or m + 2 or n + 3)
O (vx € N) (vy e N) (vm e N) (vn E N) (if m > 1 and n > 1 and x" – y = 1, then x = 3 and y = 2 and m = 2 and
n- 3)
O (*x € N) (vy € N) (m e N) (vn E N) (if x + 3 or y + 2 or m = 2 or n = 3, then x" - y = 1 or m = 1 or n = 1)

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