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Small Solutions of Congruences in a Large Number of Variables1
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- Journal:
- Canadian Mathematical Bulletin / Volume 28 / Issue 3 / 01 September 1985
- Published online by Cambridge University Press:
- 20 November 2018, pp. 295-305
- Print publication:
- 01 September 1985
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- Article
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It is shown that a system of congruences
1(x) ≡ . . . ≡ (x) = 0 (mod m)
where each
i(x) = i,(x 1, .. . ,x 2,) is a form of degree at most k has a nontrivial solution x satisfying |xi|≦cm(½)+∊(i=1,...,S)with c = c(k,r,∊), provided that ∊ > 0 and that S > S1(k,r,∊).
