170 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

Ex. ). x+vy+2=99

100x + 30y + z = 1000
Complete solution (5 4 297, 14 — 997, 80 + 70x)
Only one solution in positiv integers.

Ex. 2. x+vy+2=350

40x 4+ 20y + z = 100
General solution (12 — 19%, — 22 + 39%, 60 — 20n)
No solution in positiv integers.

Ex. 3. x+y+ 22 =40
8 + 7y + 3z = 300
Solution (— 2 + 11z, 46 — 13n, — 2 + #»)

Ex. 4. x+y+2=09
Sx + 7y + 2 = 180
Impossible (in integers).

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