Question

Of the following, which must be true whenever x^1998 = y^1998?
A. x^999=y^999
B. x^1997=y^1997
C. x^1999=y^1999
D. x^2000=y^1000

I tried plugging in 2 for x and y, but the calculator said overflow...

Answer 1

seems to me all are true.
it is an even power of x,y so

either x=y or x=-y

if x=y, then a through d are true
if x=-y, then a,b,c are true, but d is not true unless x=-y and x=+-1
so,

the answers are a,b, c for any x and y.