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PKJD-009 - ### Step 1: Understanding the ProblemThe first step is to grasp what the problem is asking. Here, the problem is to compute the value of ( A imes B ) modulo ( N ). This means I need to multiply numbers together and then find the remainder when that product is divided by another number.### Step 2: Breaking Down the ProblemTo solve this, I can break it down into smaller, more manageable parts:1. **Multiplication**: ( A imes B ) is the start.2. **Modulo Operation**: ( mod N ) involves dividing the previous result by ( N ) and finding the remainder.### Step 3: MultiplicationFirst, I'll tackle the multiplication part. Let's say ( A = 123 ) and ( B = 456 ). Multiplying these two numbers:- ( 123 imes 456 = ) ?To make this easier, I'll use the standard algorithm of multiplication:1. Multiply ( 123 ) by ( 460 ).2. Multiply ( 123 ) by ( -4 ).3. Add both results to find the product.Wait, this seems off. Actually, it's better to multiply ( 123 ) by ( 456 ) directly:- ( 123 imes 456 = 123 imes (400 + 50 + 6) = 123 imes 400 + 123 imes 50 + 123 imes 6 )Calculating each part:- ( 123 imes 400 = 49,200 )- ( 123 imes 50 = 6,150 )- ( 123 imes 6 = 738 )Adding these up: ( 49,200 + 6,150 + 738 = 56,088 )So, ( A imes B = 56,088 )### Step 4: Modulo OperationNow, I need to find ( 56,088 mod N ). Let's say ( N = 1,000 ). So, I need to find the remainder when ( 56,088 ) is divided by ( 1,000 ).This involves dividing ( 56,088 ) by ( 1,000 ) and seeing what's left:- ( 56,088 div 1,000 = 56 ) with a remainder since ( 1,000 imes 56 = 56,000 )- Remainder: ( 56,088 - 56,000 = 88 )Thus, ( A imes B mod N = 88 )### Step 5: ConclusionAfter performing the multiplication and the modulo operation, I've found that the final answer is ( 88 ).(ox{88})
2019年11月14日
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