5

Part of 1991 IberoAmerican

Problems(1)

Values of a polynomial

Source: Ibero-American Olympiad 1991, Problem 5

P(x,\, y)=2x^{2}-6xy+5y^{2}

. Let us say an integer number

a

P

if there exist integer numbers

b

c

P(b,\, c)=a

. a) Find all values of

P

lying between 1 and 100. b) Show that if

r

s

P

rs

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